Constructing formal semantics from an ontological perspective. The case of second-order logics

In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal semantics from an ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use.     

Implicit ontological commitment

Quine’s general approach is to treat ontology as a matter of what a theory says there is. This turns ontology into a question of which existential statements are consequences of that theory. This approach is contrasted favourably with the view that takes ontological commitment as a relation to things. However within the broadly Quinean approach we can distinguish different accounts, differing as to the nature of the consequence relation best suited for determining those consequences. It is suggested that Quine’s own narrowly formal account fails. Then a consideration of the necessitation approach championed by Jackson and Lewis shows that it does not do justice to the role of acknowledging consequences in determining rationality. I suggest that an approach which puts a priori consequence as the key relation does a better job. The task of spelling out the nature of a priori consequence is sketched, along with reasons to doubt the adequacy of the double indexing approach to analysing the a priori. The sorts of relations we can stand in to theories which allow us to inherit ontological commitments are touched on with a number of important philosophical strategies for introducing belief-like attitudes which nevertheless avoid ontological commitment.

The Logical Basis of the Tractarian Ontology

This paper focuses on the relation between logic and ontology. In particular, it demonstrates how classical logical theory can clarify the ontological part of Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. To this end, the work examines the adequacy of a formal system that was devised by the Polish logician, mathematician and philosopher Roman Suszko (1919–1979) as a model for the Tractatus. Following a brief explanation of the Tractarian ontology, the main ideas of Suszko’s system and its philosophical significance will be considered. The latter will be illustrated in the context of central Tractarian concepts. Finally, two implications for a better understanding of the Tractarian ontology will be pointed out.

Presentation as anti-phenomenon in Alain Badiou's Being and Event

In his magnum opus Being and Event, Alain Badiou identifies ontology with mathematics and uses a mathematical formalization of ontological discourse to generate an account of extra-ontological 'truth-events'. Informed by deconstructive critiques of the metaphysical ontologies of presence, Badiou establishes an anti-phenomenological conception of ontological presentation. Presentation's internal structure is that of an anti-phenomenon: presence's necessarily empty and insubstantial contrary. But the result is that Being and Event is riven by a fundamental methodological idealism. Badiou cannot secure the connection he wishes to establish between the formal discursive structure of mathematical ontology and extra-discursive reality. The decisive link between being and event, i.e. between Badiou's purely formal conception of ontological presentation and the extra-ontological reality of the event, is precluded by the very structure of the concept of presentation which is central to Badiou's argument.     

The Partial Identity Account of Partial Similarity Revisited

This paper provides a defence of the account of partial resemblances between properties according to which such resemblances are due to partial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to conceive of the structural universals first posited by Armstrong in order to explain partial resemblances, and focuses instead on criticisms that have been levelled against the theory (by Pautz, Eddon, Denkel and Gibb) and that apply regardless of one’s preferred ontological framework. The partial identity account is defended from these objections and, in doing so, a hitherto quite neglected connection—between the debate about partial similarity as partial identity and that concerning ontological finitism versus infinitism—is looked at in some detail.     

The ontology of intentionality I: the dependence ontological account of order: mediate and immediate moments and pieces of dependent and independent objects

This is the first of three essays which use Edmund Husserl's dependence ontology to formulate a non-Diodorean and non-Kantian temporal semantics for two-valued, first-order predicate modal languages suitable for expressing ontologies of experience (like physics and cognitive science). This essay's primary desideratum is to formulate an adequate dependence-ontological account of order. To do so it uses primitive (proper) part and (weak) foundation relations to formulate seven axioms and 28 definitions as a basis for Husserl's dependence ontological theory of relating moments. The essay distinguishes between dependence v. independence, pieces v. moments, mediate v. immediate pieces and moments, maximal v. non-maximal pieces, founded v. unfounded qualities, integrative v. disintegrative dependence, and defines the concepts of the completion of an object, the adumbrational equivalence relation of objects, moments of unity which unify objects, and relating moments which relate objects. The eight theorems [CUT90]-[CUT97] show that relating moments of unity provide an adequate account of order in terms of primitive (proper) part and (weak) foundation relations.     

On the motivations for Merleau-Ponty’s ontological research

This paper attempts to clarify Merleau-Ponty’s later work by tracing a hitherto overlooked set of concerns that were of key consequence for the formulation of his ontological research. I argue that his ontology can be understood as a response to a set of problems originating in reflections on the intersubjective use of language in dialogue, undertaken in the early 1950s. His study of dialogue disclosed a structure of meaning-formation and pointed towards a theory of truth (both recurring ontological topics) that post-Phenomenology premises could not account for. A study of dialogue shows that speakers’ positions are interchangeable, that speaking subjects are active and passive in varying degrees, and that the intentional roles of subjects and objects are liable to shift or ‘transgress’ themselves. These observations anticipate the concepts of ‘reversibility’ and ‘narcissism’, his later view of activity and passivity, and his later view of intentionality, and sharpened the need to adopt an intersubjective focus in ontological research.     

The Problem of das Man—A Simmelian Solution

Current interpretations of Heidegger's notion of das Man are caught in a dilemma: either they cannot accommodate the ontological status Heidegger accords it or they cannot explain his negative evaluation of it, in which it is treated as ontic. This paper uses Simmel's agonistic account of human sociality to integrate the ontological and the ontic, indeed perjorative aspects of Heidegger's account. Section I introduces the general problem, breaks the exclusive link of Heidegger's account to Kierkegaard and delineates the general form of a solution. Section II then sketches Simmel's conception of sociology and sociality. Section III determines what Heidegger is trying to do in Chapter Four of Division I in Being and Time in order to formulate a strictly ontological account of das Man. Section IV uses Simmel's account of sociality to build into this ontological account an inherent tendency to display the negative features Heidegger ascribes to das Man. In conclusion, section V points to how the proposed account of das Man intimates the character of fundamental ontology as nascently a form of critical theory. It also explains the extent to which Heidegger's perjorative characterisations of das Man and the Man-selbst are legitimate.     

Theory structuralism in a rigid framework

This paper develops the first parts of a logical framework for the empirical sciences, by means of a redefinition of theory structuralism as originally developed by Joseph Sneed, Wolfgang Stegmüller, and others, in the context of a ??rigid?? logic as based on a fixed (therefore rigid) ontology. The paper defends a formal conception of the empirical sciences that has an irreducible ontological basis and is unable, in general, to provide purely structural characterizations of the domain of a theory. The extreme rationalist utopia of a characterization of the real world ??up to isomorphism??, therefore, is rejected.     

A Pinch of Salt for Frege

Michael Dummett has argued that a formal semantics for our language is inadequate unless it can be shown to illuminate to our actual practice of speaking and understanding. This paper argues that Frege’s account of the semantics of predicate expressions according to which the reference of a predicate is a concept (a function from objects to truth values) has exactly the required characteristics. The first part of the paper develops a model for understanding the distinction between objects and concepts as an ontological distinction. It argues that, ontologically, we can take a Fregean function to be generated by a property detection device that can register for any object the presence or absence of that property. This provides a direct connection between the semantics of sentences and the structure of perceptual judgment. The second part of the paper deals with arguments that have been mounted against the coherence of Frege’s semantics. It argues that some of these are question begging, while others are correct in so far as Frege’s claim is untenable if we assume that the syntactic categories singular term and predicate are primary, and the ontological categories are simply projections of these syntactic categories. However, the objections dissipate once we recognize that an independent ontological characterization of the distinction is available.     

Truth,Sentential Non-Compositionalit,and Ontology

The paper attempts to clarify some fundamental aspects of an explanationof the concept of truth which is neither deflationary nor substantive.The main aspect examined in detail concerns the ontological dimension of truth, the mind/language-world connection traditionally associated with the concept of truth. It is claimed that it does not make sense to defend or reject a relatedness of truth to the ontological dimension so long as the kind of presupposed or envisaged ontology is not made explicit and critically examined. In particular, it is shown that generally an objectual ontology is – often only implicitly – presupposed, i.e., an ontology admitting objects (substances), properties, relations, sometimes also facts, events, and the like. The paper demonstrates that such an ontology derives from the Principle of Semantic Sentential Compositionality and that this principle should be rejected. It introduces instead the Principle of Semantic Sentential Contextuality (or Context Principle) as the semantic basis of a new ontology, an ontology of primary states of affairs. After sketching such an ontology, it is shown that the relatedness of truth to the ontological dimension becomes intelligible.     

Thinking about non‐being∗

There are genuine references to non‐existent objects, as can be seen through elucidating reference in common language and applying the criteria enumerated to expressions used in writing and speaking about fiction. The concept of a fictitious entity is simply accepted in the adoption of the ‘language‐game’ of fiction and has no undesirable ontological consequences. To think otherwise is to fail to attend to the conceptual status of such talk. Accounts of fictional discourse by Russell, Ryle, and Chisholm are found objectionable. The concept of existence is touched on, and consequences concerning reference to abstract and other objects and also concerning method in ontology mentioned.     

No two entities without identity

In a naïve realist approach to reading an ontology off the models of a physical theory, the invariance of a given theory under permutations of its property-bearing objects entails the existence of distinct possible worlds from amongst which the theory cannot choose. A brand of Ontic Structural Realism (OSR) attempts to avoid this consequence by denying that objects possess primitive identity, and thus worlds with property values permuted amongst those objects are really one and the same world. Assuming that any successful ontology of objects is able to describe a universe containing a determinate number of them, I argue that no version of OSR which both retains objects and understands ‘structure’ in terms of relations can be successful. This follows from the fact that no set of relational facts is sufficient to fix the cardinality of the collection of objects implied by those facts. More broadly, I offer reasons to believe that no version of OSR is compatible with the existence of objects, no matter how ontologically derivative they are taken to be. Any such account would have to attribute a definite cardinality to a collection of objects while denying that those objects are possessed of a primitive identity. With no compelling reason to abandon the classical conception of cardinality, such an attribution is incoherent.     

The therapy of power and the power of therapy

Constructivism's ontology-based epistemology considers reality an expression of strictly subjective cognitive processes. Taking the conceptpower as an example, theeigen-dynamics of connecting these subjective constructions of reality in the socialization process are compared with this ontological epistemology. The qualities of such dynamics cannot be concluded from ontology. An alternative approach is taken here which proceeds from a sociological orientation, describes the structure and dynamics of power relations in the differentiation process of social systems, and applies to families and family therapy for an example. The conclusion draws attention to the necessity of a critical notion of power to permit discussion of ethical questions in the context of systems theory as well.Originally published as part of a special issue on the power metaphor guestedited by Klaus G. Deissler inZeitschrift fur systemische Therapie (1986),4, 243–252. Translated by S. Awodey.     

Mereological bundle theory and the identity of indiscernibles

Paul (Noûs 36:578–596, 2002; Noûs 40:623–659, 2006, The Handbook of Mereology, forthcoming) has argued for a bundle theory of objects that analyzes the bundling relation between properties and objects in terms of parthood relations. In this paper I argue that any mereological bundle theory with the explanatory power of Paul’s theory will entail the principle of the identity of indiscernibles (PII). This is problematic, since similar bundle theories seem to fall to Max Black’s two sphere counterexample to (PII). I argue, however, that a fully developed mereological bundle theory provides a new way of interpreting Black’s two sphere universe that dispels the counterexample. I argue that this solution to Black’s puzzle is superior to other solutions on offer, and consequently that mereological bundle theory is an attractive ontological strategy for friends of (PII).     

A defence of informational structural realism

This is the revised version of an invited keynote lecture delivered at the 1st Australian Computing and Philosophy Conference (CAP@AU; the Australian National University in Canberra, 31 October–2 November, 2003). The paper is divided into two parts. The first part defends an informational approach to structural realism. It does so in three steps. First, it is shown that, within the debate about structural realism (SR), epistemic (ESR) and ontic (OSR) structural realism are reconcilable. It follows that a version of OSR is defensible from a structuralist-friendly position. Second, it is argued that a version of OSR is also plausible, because not all relata (structured entities) are logically prior to relations (structures). Third, it is shown that a version of OSR is also applicable to both sub-observable (unobservable and instrumentally-only observable) and observable entities, by developing its ontology of structural objects in terms of informational objects. The outcome is informational structural realism, a version of OSR supporting the ontological commitment to a view of the world as the totality of informational objects dynamically interacting with each other. The paper has been discussed by several colleagues and, in the second half, ten objections that have been moved to the proposal are answered in order to clarify it further.     

Emergence for Nihilists

I defend mereological nihilism, the view that there are no composite objects, against a challenge from ontological emergence, the view that some things have properties that are ‘something over and above’ the properties of their parts. As the nihilist does not believe in composite wholes, there is nothing in the nihilist's ontology to instantiate emergent properties – or so the challenge goes. However, I argue that some simples (taken together) can collectively instantiate an emergent property, so the nihilist's ontology can in fact accommodate emergent properties. Furthermore, I show that employing plural instantiation does not bloat the nihilist's ontology or ideology.     

TRANSVALUATIONISM ABOUT VAGUENESS: A PROGRESS REPORT

The philosophical account of vagueness I call “transvaluationism” makes three fundamental claims. First, vagueness is logically incoherent in a certain way: it essentially involves mutually unsatisfiable requirements that govern vague language, vague thought‐content, and putative vague objects and properties. Second, vagueness in language and thought (i.e., semantic vagueness) is a genuine phenomenon despite possessing this form of incoherence—and is viable, legitimate, and indeed indispensable. Third, vagueness as a feature of objects, properties, or relations (i.e., ontological vagueness) is impossible, because of the mutually unsatisfiable conditions that such putative items would have to meet. In this paper I set forth the core claims of transvaluationism in a way that acknowledges and explicitly addresses a challenging critique by Timothy Williamson of my prior attempts to articulate and defend this approach to vagueness. I sketch my favored approach to truth and ontological commitment, and I explain how it accommodates the impossibility of ontological vagueness. I argue that any approach to the logic and semantics of vagueness that both (i) eschews epistemicism and (ii) thoroughly avoids positing any arbitrary sharp boundaries (either first‐order or higher‐order) will have to be not an alternative to transvaluationism but an implementation of it. I sketch my reasons for repudiating epistemicism. I briefly describe my current thinking about how to accommodate intentional mental properties with vague content within an ontology that eschews ontological vagueness. And I revisit the idea, which played a key role in my earlier articulations of transvaluationism, that moral conflicts provide an illuminating model for understanding vagueness.     

Ontological categories guide young children's inductions of word meaning: object terms and substance terms

Three experiments assessed the possibility, suggested by Quine (1960, 1969) among others, that the ontology underlying natural language is induced in the course of language learning, rather than constraining learning from the beginning. Specifically, we assessed whether the ontological distinction between objects and non-solid substances conditions projection of word meanings prior to the child's mastery of count/mass syntax. Experiments 1 and 2 contrasted unfamiliar objects with unfamiliar substances in a word-learning task. Two-year-old subjects' projection of the novel word to new objects respected the shape and number of the original referent. In contrast, their projection of new words for non-solid substances ignored shape and number. There were no effects of the child's knowledge of count/mass syntax, nor of the syntactic context in which the new word was presented. Experiment 3 revealed that children's natural biases in the absence of naming do not lead to the same pattern of results. We argue that these data militate against Quine's conjecture.     

The ontology of intentionality II: dependence ontology as prolegomenon to noetic modal semantics

This is the second in a sequence of three essays which axiomatize and apply Edmund Husserl's dependence ontology of parts and wholes as a non-Diodorean, non-Kantian temporal semantics for first-order predicate modal languages. The Ontology of Intentionality I introduced enough of Husserl's dependence-ontology of parts and wholes to formulate his account of order as effected by relating moments of unity, and The Ontology of Intentionality II extends that axiomatic dependence-ontology far enough to enable its semantic application. Formalizing the compatibility [Vereinbarkeit] relation implicated in Husserl's notorious doctrine of impossible meanings, the essay introduces a compatibility restriction on relations to formulate Husserl's distinction between singular [einheitliche] and plural [mehrheitliche] objects, using plural relating moments to define first-order versions of Husserl's notions of relation complexes (i.e. Sachverhalte), abstracta of n-ary relation complexes, categorial relations, abstract eide as unifications of categorial relations, semantic domains as completions of abstract eide, and material regions as semantic domains which are compatibility upper bounds of categorial relations. These concepts will enable the formal dependence-ontological noetic semantics for two-valued, first-order modal languages introduced in the sequel Two-Valued Logics of Intentionality, the third essay in the sequence.