Functionalism about Truth and the Metaphysics of Reduction

Functionalism about truth is the view that truth is an explanatorily significant but multiply-realizable property. According to this view the properties that realize truth vary from domain to domain, but the property of truth is a single, higher-order, domain insensitive property. We argue that this view faces a challenge similar to the one that Jaegwon Kim laid out for the multiple realization thesis. The challenge is that the higher-order property of truth is equivalent to an explanatorily idle disjunction of its realization bases. This consequence undermines the alethic functionalists’ non-deflationary ambitions. A plausible response to Kim’s argument fails to carry over to alethic functionalism on account of significant differences between alethic functionalism and psychological functionalism. Lynch’s revised view in his book Truth as One and Many (2009) fails to answer our challenge. The upshot is that, while mental functionalism may survive Kim’s argument, it mortally wounds functionalism about truth.     

Alethic Functionalism,Manifestation, and the Nature of Truth

Michael Lynch has recently proposed an updated version of alethic functionalism according to which the relation between truth per se and lower-level truth properties is not the realization relation, as might be expected, and as Lynch himself formerly held, but the manifestation relation. I argue that the manifestation relation is merely a resemblance relation and is inadequate to properly relate truth per se to lower-level truth properties. I also argue that alethic functionalism does not justify the claim that truth per se exists, or that truth per se is a functional property. Finally, I suggest a replacement for the manifestation relation. I argue that the resulting theory is a strict improvement over alethic functionalism on two counts, but that the improved theory does not justify the claim that truth per se exists. Since no further improvements to the theory are apparent, the prospects for alethic functionalism are dim.     

Theories and Theories of Truth

Formal theories, as in logic and mathematics, are sets of sentences closed under logical consequence. Philosophical theories, like scientific theories, are often far less formal. There are many axiomatic theories of the truth predicate for certain formal languages; on analogy with these, some philosophers (most notably Paul Horwich) have proposed axiomatic theories of the property of truth. Though in many ways similar to logical theories, axiomatic theories of truth must be different in several nontrivial ways. I explore what an axiomatic theory of truth would look like. Because Horwich’s is the most prominent, I examine his theory and argue that it fails as a theory of truth. Such a theory is adequate if, given a suitable base theory, every fact about truth is a consequence of the axioms of the theory. I show, using an argument analogous to Gödel’s incompleteness proofs, that no axiomatic theory of truth could ever be adequate. I also argue that a certain class of generalizations cannot be consequences of the theory.     

Can realists know that they know?

Realists typically suppose that nonepistemic truth is an independent condition on propositional knowledge. Few philosophers, however, have seriously questioned the meta-epistemic consequences of combining alethic and epistemic variants of realism. In this paper I aim to show that the truth condition in the customary definition of knowledge presents an important problem for the realist at higher epistemic levels. According to my argument, traditional epistemic-logical analyses of metaknowledge fail because of their extensionalism and certain presuppositions they have about the satisfaction of the truth condition. I further suggest that we need a different approach to metaknowledge if (1) we want to retain alethic realism, and (2) we want our epistemological accounts to adequately explicate the meta-epistemic states of actual, evidence-bound cognitive agents. This paper greatly benefited from the comments and criticisms of an anonymous referee for Acta Analytica.     

An Old Solution to the Problem of Mixed Atomics

This paper examines a difficulty for various forms of truth pluralism, known in the literature as the problem of ‘mixed atomics’. It is argued that two prominent attempts to respond to the difficulty—those of Jeremy Wyatt and Gila Sher—fail. In their place, an alternative is offered based on parts of Crispin Wright’s Truth and Objectivity programme. It is argued that the Wrightian approach works because it substitutes traditional conceptions of truth-relevant properties, for example correspondence and coherence, for criteria of objectivity pertaining to discursive practices. This allows us to give expression to the nuanced way in which the pluralist wants to treat mixed atomics.     

Conceptual Schemes Revisited: Davidsonian Metaphysical Pluralism

Davidson’s 1974 argument denying the possibility of incommensurable conceptual schemes is widely interpreted as entailing a denial of metaphysical pluralism. Speakers may group objects differently or have different beliefs about the world, but there is just one world. I argue there is tension arising from three aspects of Davidson’s philosophy: (1) the 1974 argument against conceptual schemes; (2) Davidson’s more recent emphasis on primitive triangulation as a necessary condition for thought and language; and (3) Davidson’s semantic approach to metaphysics, what he calls ‘the method of truth in metaphysics’. After elucidating the tension, I argue the tension can be resolved while preserving at least two major tenets of Davidson’s philosophy: (1) conceptual schemes do not carve an uninterpreted reality into different worlds and (2) truth is objective and non-epistemic. I argue Davidson is implicitly committed to a plurality of worlds.     

Local collection and end-extensions of models of compositional truth

We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the case of the induction scheme.We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate.     

Deflationist Truth is Substantial

Deflationism is usually thought to differ from the correspondence theory over whether truth is a substantial property. However, I argue that this notion of a ‘substantial property’ is tendentious. I further argue that the Equivalence Schema alone is sufficient to lead to idealism when combined with a pragmatist theory of truth. Deflationism thus has more powerful metaphysical implications than is generally thought and itself amounts to a kind of correspondence theory.     

A semantic study of the first-order predicate logic with uncertainty involved

In this paper, we provide a semantic study of the first-order predicate logic for situations involving uncertainty. We introduce the concepts of uncertain predicate proposition, uncertain predicate formula, uncertain interpretation and degree of truth in the framework of uncertainty theory. Compared with classical predicate formula taking true value in \(\{0,1\}\) , the degree of truth of uncertain predicate formula may take any value in the unit interval \([0,1]\) . We also show that the uncertain first-order predicate logic is consistent with the classical first-order predicate logic on some laws of the degree of truth.     

一种新的中介真值程度的度量方法及模糊谓词的分解

以中介数学系统为背景, 为处理现实生活中普遍存在的模糊现象提供一种度量逻辑真值程度的新方法. 在建立了谓词的标准度概念后, 描述了谓词的真值与对应的数值区域之间的关系; 采用距离的概念, 并以对应谓词真值的数值区域长度为基准, 给出了一维情形下的个体真值程度函数以及基于真值程度函数的一元谓词的表示法.又在提出了λ-真值程度截集、数与谓词的乘积概念后,给出了关于一元模糊谓词的中介分解定理, 从而建立了一元模糊谓词与清晰谓词间的量化关系.应用示例表明:真值程度函数的定义具有计算机可以处理的定量形式且具有客观性和普适性的特点.     

A critical assessment of truth functional modification and its use in approximate reasoning

We examine the inconsistencies in the current notion of fuzzy truth values and show how these have arisen from an attempt to equate two separate concepts. We argue that any approximate reasoning system based on truth functional modification is redundnat and inefficient.     

Extended Modal Dimensionalism

Modal dimensionalism (MD) is realism about spaces, times and worlds—metaphysical indices that make objects spatial, temporal and modal, respectively, and that play the role of alethic relativizers, i.e. items to which matters of truth are relativized. This paper examines several arguments against MD and shows that MD offers a feasible way to understand modal discourse.     

一阶模糊谓词逻辑公式的解释模型真度理论及其应用

基于一阶模糊谓词逻辑公式的有限和可数解释真度的理论,引入了一阶模糊谓词逻辑公式的解释模型及解释模型真度的概念,并讨论了它们的一系列性质及其在近似推理中的应用.     

Register computations on ordinals

We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zermelo-Fraenkel axioms ZFC. This allows the following characterization of computable sets: a set of ordinals is ordinal register computable if and only if it is an element of Gödel’s constructible universe L.     

Remarks on the Interest-relative Theory of Vagueness

I discuss the interest-relative account of vagueness and argue for a distinction between relational vague predicates and non-relational vague predicates depending on the kind of properties expressed by them. The strategy rests on three arguments arising from the existence of clear cases of a vague predicate, from contexts in which a different answer is required for questions about whether a vague predicate applies to an item, and whether such an item satisfies the interest of an agent, and from cases where an object changes up to the point of becoming P, where P is a vague predicate. In the second part of the paper, I distinguish between relational properties and non-relational properties, and I argue for the view that some vague predicates can express non-relational properties, comparative relational properties and interest-relative properties. On the basis of these arguments, I conclude that vagueness cannot be reduced to interest-relativity.     

Solutions of fixed sign of higher-order inhomogeneous equations of mixed elliptic-hyperbolic type

For a higher-order inhomogeneous equation of mixed elliptic-hyperbolic type, the property of the solution to be of fixed sign is established, depending on the sign of the right-hand side.     

Conservative extension of polyadic MV-algebras to polyadic pavelka algebras

In this paper we prove polyadic counterparts of the Hájek, Paris and Shepherdson's conservative extension theorems of Łukasiewicz predicate logic to rational Pavelka predicate logic. We also discuss the algebraic correspondents of the provability and truth degree for polyadic MV-algebras and prove a representation theorem similar to the one for polyadic Pavelka algebras.     

Interpolation in superintuitionistic predicate logics with equality

It is shown that the Craig interpolation property and the Beth property are preserved under passage from a superintuitionistic predicate logic to its extension via standard axioms for equality, and under adding formulas of pure equality as new axioms. We find an infinite independent set of formulas which, though not equivalent to formulas of pure equality, may likewise be added as new axiom schemes without loss of the interpolation, or Beth, property. The formulas are used to construct a continuum of logics with equality, which are intermediate between the intuitionistic and classical ones, having the interpolation property. Moreover, an equality-free fragment of the logics constructed is an intuitionistic predicate logic, and formulas of pure equality satisfy all axioms of the classical predicate logic. Supported by RFFR grant No. 96-01-01552. Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 543–561, September–October, 1997.     

Arguing About the Effectiveness of Assessments for the Classroom

Approaches to test score use and test purpose lack the well-developed methodological guidelines and established sources of evidence available for intended score interpretation. We argue in this paper that this lack fails to reflect the ultimate purpose of a test score—to help solve an important problem faced by intended test users. We explore the treatment of intended test purpose and test score use under the chain of assumption/inferences perspective identified within an argument-based approach to validity. Next, we revisit the notion of test score use and argue that, at least for classroom assessments based on complex constructs, such as learning progressions in math and science, test score use can be more effectively conceptualized as part of a potential solution to solving a problem, or “job-to-be-done.”. We argue for shifting from the definition of validity to the concept of effectiveness. Finally, we illustrate an argument- based approach to test score effectiveness by contrasting effectiveness arguments for interim assessments based on a conventional test blueprint or a test blueprint augmented with learning progressions.     

The dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations

The a priori boundedness principle is proved for the Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Several sufficient conditions of solvability of the Dirichlet problem under consideration are derived from the a priori boundedness principle. The proof of the a priori boundedness principle is based on the Agarwal-Kiguradze type theorems, which guarantee the existence of the Fredholm property for strongly singular higher-order linear differential equations with argument deviations under the two-point conjugate and right-focal boundary conditions.