A Temporal Logic for Sortals

With the past and future tense propositional operators in its syntax, a formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. A completeness proof for the system is constructed and its absolute consistency proved. The completeness proof is given relative to a notion of logical validity provided by an intensional semantic system, which assumes an approach to sortals from a modern form of conceptualism.     

A Modal Sortal Logic

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.     

A Two Dimensional Tense-modal Sortal Logic

We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.     

Events, Sortals, and the Mind–Body Problem

In recent decades, a view of identity I call Sortalism has gained popularity. According to this view, if a is identical to b, then there is some sortal S such that a is the same S as b. Sortalism has typically been discussed with respect to the identity of objects. I argue that the motivations for Sortalism about objectidentity apply equally well to event-identity. But Sortalism about event-identity poses a serious threat to the view that mental events are token identical to physical events: A particular mental event m is identical with a particular physical event p only if there is a sortal S such that m and p are both Ss. If there is no such sortal, the doctrine of token-identity is not true. I argue here that we have no good reason for thinking that there is any such sortal.     

Physicalism and the sortalist conception of objects

Many hold an Aristotelian metaphysic of objects: fundamentally, objects fall under sortals and have persistence conditions befitting their sort. Though sometimes offered as a theory of material objects, I argue this view is in fact incompatible with physicalism. Call a ‘sortal’ a kind of object, a ‘sortal identity’ a particular’s nature specified in sortal terms, and ‘sortal properties’ properties that are determined by an object’s sortal identity, such as its persistence conditions. From here the argument runs as follows. Something is physical only if it is physically fundamental or is determined by what is physically fundamental (P1), but sortal identities and properties are neither physically fundamental (P2) nor determined by the physically fundamental (P3). I defend each premise in turn. P1 falls out of the standard conception of physicalism. Rejecting P2 is tantamount to positing Aristotelian substantial forms and formal causes—which are themselves incompatible with physicalism. I defend P3 by showing that extant solutions to “the grounding problem”—the problem of showing how (nonfundamental) sortal properties are determined by (nonsortal) physical properties—are either physicalistically unacceptable, or else physicalistically acceptable but opposed to the sortalist metaphysic.     

Realization, Micro-Realization, and Coincidence

Let thin properties be properties shared by coincident entities, e.g., a person and her body, and thick properties ones that are not shared. Thick properties entail sortal properties, e.g., being a person, and the associated persistence conditions. On the first account of realization defined here, the realized property and its realizers will belong to the same individual. This restricts the physical realizers of mental properties, which are thick, to thick physical properties. We also need a sense in which mental properties can be realized in thin physical properties shared by a person and her body. Defining this in turn requires defining a sense in which the instantiations of sortal properties and of thick properties are realized in micro-structural states of affairs. A fourth notion of realization is needed to allow for the possibility of coincident entities that share a sortal property, e.g., coincident persons.     

Coercion and pragmatic presuppositions

In Category Mistakes, Magidor proposes that sortal restrictions should be viewed as pragmatic presuppositions. This contrasts with recent linguistic theories of successfully resolved category mistakes, e.g. coercions or copredication. It has been argued that for the proper treatment of such examples, sortal restrictions should be expressed by semantic presuppositions since they need to interact with compositional semantics. I explore possible ways in which Magidor’s theory could be extended to explain examples of coercion and copredication. The outcome of the discussion is that incorporation of these facts into Magidor’s pragmatic system might be possible, but ecessitates choices that are far from trivial.     

Criteria of identity without sortals

Many philosophers believe that the criteria of identity over time for ordinary objects entail that such objects are permanent members of certain sortal kinds. The sortal kinds in question have come to be known as substance sortal kinds. But in this article, I defend a criterion of identity that is suited to phasalism, the view that alleged substance sortals are in fact phase sortals. The criterion I defend is a sortal-weighted version of a change-minimizing criterion first discussed by Eli Hirsch. I present this criterion and then argue that it withstands attempts to show that it is inferior to non-phasalist rivals.     

客体连续性的加工机制

把先前和现在遇到的客体视为同一个体的现象就可以称为客体连续性。目前对客体连续性的形成主要存在四种解释机制：相似理论、时空理论、种类理论和因果理论。研究者对时空理论中时空信息和客体表面特征信息, 种类理论和因果理论在此过程中所起的作用存在争论。今后应构建相似、种类、因果理论的实验范式, 改进时空、种类和因果理论实验设计的不足并把客体连续性的研究从视觉领域拓展到到嗅觉、听觉等领域。     

A New–old Characterisation of Logical Knowledge

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ‘sortal terms’, two theories that will feature prominently. Second, we propose that logic comprises four ‘momental sectors’: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (in)valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its ‘external’ negation not-R; and the assertion of R in the pair of propositions ‘it is (un)true that R’ belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended.     

Using logical relevance for question answering

We propose a novel method of determining the appropriateness of an answer to a question through a proof of logical relevance rather than a logical proof of truth. We define logical relevance as the idea that answers should not be considered as absolutely true or false in relation to a question, but should be considered true more flexibly in a sliding scale of aptness. This enables us to reason rigorously about the appropriateness of an answer even in cases where the sources we are getting answers from are incomplete or inconsistent or contain errors. We show how logical relevance can be implemented through the use of measured simplification, a form of constraint relaxation, in order to seek a logical proof than an answer is in fact an answer to a particular question. We then give an example of such an implementation providing a set of specific rules for this purpose.     

Proof Theory for Functional Modal Logic

We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \(\mathord {\sim }\mathord {\Box }A\equiv \mathord {\Box }\mathord {\sim }A\). We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.     

On the consistency of a three-valued logical calculus

[This résumé was published in English in Matematicheskii Sbornik along with the article.]The present paper contains an investigation of a three-valued logical calculus (the system) previously described by the author [Recueil Mathématique 4 (46), 2 (1938)].A constructive consistence proof is given for a part of this calculus rendering the results previously published concerning the Russell paradox. A method for a non-constructive completeness proof for the complete calculus is briefly indicated.     

Sortal concepts and causal continuity: comment of Rips, Blok, and Newman (2006)

L. J. Rips, S. Blok, and G. Newman (2006) proposed that singular concepts, which support the tracing of individual objects across their existence, are governed by a principle of causal continuity. They purported to show that causal continuity is better than existing theories at explaining judgments of the persistence of individual objects. This article makes 3 points. First, the construct of causal connectedness entails a wide variety of different explanatory factors; calling them all causal has questionable explanatory value. There is little evidence that the ultimate basis for identity judgments in many cases is causal. Second, the authors suggest that causal knowledge is indeed important to identity, but that it is important in the context of sortal concepts; different causal information matters for different kinds of things. Finally, the authors consider whether causal knowledge or sortal concepts are more fundamental to tracing individual identity, that is, whether causal knowledge is necessary for identity judgments. The authors appeal to research in developmental psychology that has begun to address this debate, supporting the primacy of sortal concepts. Although there continues to be shortcomings of all theories of object persistence, it is not clear that the causal continuer theory brings new clarity to the puzzle.     

The Proofs Of The Grundgedanke In Wittgenstein's Tractatus

The Tractatus contains twodifferent proofs of the Grundgedanke, or thenonreferentiality of logical constants. In thispaper, I explicate the first proof in TLP 5.4s andreconstruct the less explicitly stated second proof. My explication of the first proof shows it to beelegant but based on an invalid inference. In myreconstruction of the second proof, the main argumentis that the sign of a logical constant does not denotebecause it possesses the punctuation-mark-nature. Andit possesses the punctuation-mark-nature because,given the analyticity thesis in TLP 5, one canestablish for everyday language an adequate symbolismwith N as the sole fundamental operation such that itssign is a bar indicating merely the order and scope ofits application.     

Truth Values and Proof Theory

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.     

The sortal resemblance problem

Is it possible to characterize the sortal essence of Fs for a sortal concept F solely in terms of a criterion of identity C for F? That is, can the question ‘What sort of thing are Fs?’ be answered by saying that Fs are essentially those things whose identity can be assessed in terms of C? This paper presents a case study supporting a negative answer to these questions by critically examining the neo-Fregean suggestion that cardinal numbers can be fully characterized as those things whose identity can be assessed in terms of one-one correspondence between concepts.     

The Justification of the Logical Laws Revisited

The proof-theoretic analysis of logical semantics undermines the received view of proof theory as being concerned with symbols devoid of meaning, and of model theory as the sole branch of logical theory entitled to access the realm of semantics. The basic tenet of proof-theoretic semantics is that meaning is given by some rules of proofs, in terms of which all logical laws can be justified and the notion of logical consequence explained. In this paper an attempt will be made to unravel some aspects of the issue and to show that this justification as it stands is untenable, for it relies on a formalistic conception of meaning and fails to recognise the fundamental distinction between semantic definitions and rules of inference. It is also briefly suggested that the profound connection between meaning and proofs should be approached by first reconsidering our very notion of proof.     

Logical and psychological partitioning of mind: Depicting the same map?

The aim of this paper is to demonstrate that empirically delimited structures of mind are also differentiable by means of systematic logical analysis. For the sake of this aim, the paper first summarizes Demetriou’s theory of cognitive organization and growth. This theory assumes that the mind is a multistructural entity that develops across three fronts: the processing system that constrains processing potentials, a set of specialized structural systems (SSSs) that guide processing within different reality and knowledge domains, and a hypercognitive system that monitors and controls the functioning of all other systems. The second part of the paper focuses on the SSSs, which are the target of our logical analysis, and it summarizes a series of empirical studies demonstrating their autonomous operation. The third part develops the logical proof showing that each SSS involves a kernel element that cannot be reduced to standard logic or to any other SSS. The implications of this analysis for the general theory of knowledge and cognitive development are discussed.