This chapter contains sections titled: The Syntax and Semantics of Complex Sortal Terms On the Identity of Sorts.

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. (shrink)

Taking into account significant developments in the metaphysical thinking of E. J. Lowe over the past 20 years, _More Kinds of Being:A Further Study of Individuation, Identity, and the Logic of Sortal Terms_ presents a thorough reworking and expansion of the 1989 edition of _Kinds of Being_ Brings many of the original ideas and arguments put forth in _Kinds of Being_ thoroughly up to date in light of new developments Features a thorough reworking and expansion of the earlier work, (...) rather than just a new edition Reflects the author's conversion to what he calls 'the four-category ontology,' a metaphysical system that takes its inspiration from Aristotle Provides a unified discussion of individuation and identity that should prove to be essential reading for philosophers working in metaphysics. (shrink)

Book review of 'More Kinds of Being: A Further Study of Individuation, Identity, and the Logic of Sortal Terms'. By E. J. LOWE.

Sortal concepts are at the center of certain logical discussions and have played a significant role in solutions to particular problems in philosophy. Apart from logic and philosophy, the study of sortal concepts has found its place in specific fields of psychology, such as the theory of infant cognitive development and the theory of human perception. In this monograph, different formal logics for sortal concepts and sortal-related logical notions are characterized. Most of these logics are intensional (...) in nature and possess, in addition, a bidimensional character. That is, they simultaneously represent two different logical dimensions. In most cases, the dimensions are those of time and natural necessity, and, in other cases, those of time and epistemic necessity. Another feature of the logics in question concerns second-order quantification over sortal concepts, a logical notion that is also represented in the logics. Some of the logics adopt a constant domain interpretation, others a varying domain interpretation of such quantification. Two of the above bidimensional logics are philosophically grounded on predication sortalism, that is, on the philosophical view that predication necessarily requires sortal concepts. Another bidimensional logic constitutes a logic for complex sortal predicates. These three sorts of logics are among the important novelties of this work since logics with similar features have not been developed up to now, and they might be instrumental for the solution of philosophically significant problems regarding sortal predicates. The book assumes a modern variant of conceptualism as a philosophical background. For this reason, the approach to sortal predicates is in terms of sortal concepts. Concepts, in general, are here understood as intersubjective realizable cognitive capacities. The proper features of sortal concepts are determined by an analysis of the main features of sortal predicates. Posterior to this analysis, the sortal-related logical notions represented in the above logics are discussed. There is also a discussion on the extent to which the set-theoretic formal semantic systems of the book capture different aspects of the conceptualist approach to sortals. These different semantic frameworks are also related to realist and nominalist approaches to sortal predicates, and possible modifications to them are considered that might represent those alternative approaches. (shrink)

Sortal terms, such as table or horse, are count nouns (akin to a basic-level terms). According to some theories, the meaning of sortals provides conditions for telling objects apart (individuating objects, e.g., telling one table from a second) and for identifying objects over time (e.g., determining that a particular horse at one time is the same horse at another). A number of psychologists have proposed that sortal concepts likewise provide psychologically real conditions for individuating and identifying (...) things. However, this paper reports five experiments that cast doubt on these psychological claims. Experiments 1-3 suggest that sortal concepts do not determine when an object ceases to exist and therefore do not decide when the object can no longer be identical to a later one. Experiments 4-5 similarly suggest that sortal concepts do not provide determinate conditions for individuating objects. For example, they do not always decide whether a room contains one table or two. All five experiments feature ordinary objects undergoing ordinary changes. (shrink)

Language—often said to set human beings apart from other animals—has resisted explanation in terms of evolution. Language has—among others—two fundamental and distinctive features: syntax and the ability to express non-present actions and events. We suggest that the relation between this representation (of non-present action) and syntax can be analyzed as a relation between a function and a structure to fulfill this function. The strategy of the paper is to ask if there is any evidence of pre-linguistic communication (...) that fulfills the function of communicating an absent action. We identify a structural similarity between understanding indexes of past actions of conspecifics (who did what to whom) and one of the simplest and most paradigmatic linguistic syntactic patterns – that of the simple transitive sentence. When a human being infers past events from an index (i.e., a trace, the conditions of a conspecifics or an animal, a constellation or an object) the interpreters’ comprehension must rely on concepts similar in structure and function to the ‘thematic roles’ believed to underpin the comprehension of linguistic syntax: in his or her mind the idea of a past action or event emerges along with thematic role-like concepts; in the case of the presentation of, e.g., a hunting trophy, the presenter could be understood to be an agent (subject) and the trophy a patient (direct object), while the past action killed is implied by the condition of the object and its possession by the presenter. We discuss whether both the presentation of a trophy and linguistic syntax might have emerged independently while having the same function (to represent a past action) or whether the presentation of an index of a deed could constitute a precursor of language. Both possibilities shed new light on early, and maybe first, language use. (shrink)

This study looks at the syntax of conversational same turn self-repair in Indonesian. STSR is the process by which speakers make alterations to the turn in progress. Patterns of repetition in STSR allow us to determine which syntactic categories speakers make use of in organizing self-repair. Previously observed cross-linguistic variation in this area has been explained in terms of projectability. The majority of Indonesian repairs prove to be limited in scope to a single word or a single immediate (...) constituent. However, larger scope recycling involving constituents such as clause and verb phrase do occur. Indonesian findings are compared with those of previously published studies of other languages. The results support an interpretation in terms of projectability. (shrink)

Anil Gupta's slightly revised 1977 Pittsburgh doctoral dissertation is not a linguistic investigation of common nouns. There is no thorough attempt to organize and explain data about common nouns in natural languages. Gupta's goal is to develop and to defend formal modal languages and logics useful for the representation and defense of metaphysical theses on topics such as the structure of individuals, sorts or kinds, substances, and essences. He does, however, develop the special features of his formal syntax and (...) semantics on the basis of two theses about common nouns in our natural languages. Geach's work suggests the first thesis that properly expressed identity statements are of the form: b is the same K as c, where K is a common noun. Because the individual variables bound by quantifiers must be capable of being terms of an identity relation, this first thesis leads Gupta to require quantifiers to link individual variables with common noun expressions. Thus in his formal languages we can only express: "every K is _____" or "some K is _____" where K is syntactically part of the quantifier. We can call this "sortal quantification." Hence, "Every K is P" and "Some K is P" are not even expressible as "If anything is K then it is P" or "Something is K and P," let alone equivalent to such ill-formed expressions in his languages. Gupta's book is a useful introduction to the syntax and semantics for languages with this non-standard sortal quantification for those already familiar with the syntax and formal semantics of first order extensional and modal languages with standard quantifiers. Those unfamiliar with standard formal languages and model structure semantics will find Gupta's provocative metaphysical theories and conjectures inaccessible. (shrink)

Much has been said about the logical difference between rules and principles, yet few authors have focused on the distinct logical connectives linking the normative conditions of both norms. I intend to demonstrate that principles, unlike rules, are norms whose antecedents are linguistically formulated in a generic fashion, and thus logically described as inclusive disjunctions. This core feature incorporates the relevance criteria of normative antecedents into the world of principles and also explains their aptitude to conflict with opposing norms, namely (...) that their consequents are fulfilled to varying extents more frequently than those of rules. I conclude that the property of genericity should be predicated to the norm antecedent of principles, more precisely to the hypothetical action. This is of paramount importance to explain, in terms of logical implication and exclusion, the expansibility of competing principles, in contrast with the exclusive character of conflicting rules. (shrink)

The representation of history continues to evolve in the domain of museum exhibitions. This evolution is informed in part by the creation of new display methods—many of which depart from the traditional conventions used to achieve the “museum effect”—in part by an increased attention to the museum–visitor relationship. In this context the ethical force of bearing witness, at times a crucial aspect of the museum experience, has emerged as a particularly compelling issue. In seeking to represent and address atrocity, injustice, (...) and the abrogation of human rights, museums have the potential to become “sites of conscience” and to encourage “historical consciousness.” Through a series of three exhibitions devoted to slavery, the New-York Historical Society demonstrated how such sites can be constructed and how objects can be deployed to represent extreme or “limit cases.” In this review/essay I investigate and interrogate these exhibitions, looking closely at the use of objects as a source of “indirect testimony” and at the “dialogical situation” that might arise in an encounter among objects, exhibit narratives, and visitors. Thinking in terms of point of view, I look at the variety of rhetorical platforms from which objects speak in these exhibitions; thinking in terms of syntax, I look at the effects of ordering and of the radical juxtaposition of objects; thinking in terms of irony, I look at the provocations of double-voiced narratives and at how objects are used to support those historical sentences. (shrink)

Recent work on the acquisition of number words has emphasized the importance of integrating linguistic and developmental perspectives [Musolino, J. (2004). The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. Cognition93, 1-41; Papafragou, A., Musolino, J. (2003). Scalar implicatures: Scalar implicatures: Experiments at the semantics-pragmatics interface. Cognition, 86, 253-282; Hurewitz, F., Papafragou, A., Gleitman, L., Gelman, R. (2006). Asymmetries in the acquisition of numbers and quantifiers. Language Learning and Development, 2, 76-97; Huang, Y. T., Snedeker, J., Spelke, (...) L. (submitted for publication). What exactly do numbers mean?]. Specifically, these studies have shown that data from experimental investigations of child language can be used to illuminate core theoretical issues in the semantic and pragmatic analysis of number terms. In this article, I extend this approach to the logico-syntactic properties of number words, focusing on the way numerals interact with each other (e.g. Three boys are holding two balloons) as well as with other quantified expressions (e.g. Three boys are holding each balloon). On the basis of their intuitions, linguists have claimed that such sentences give rise to at least four different interpretations, reflecting the complexity of the linguistic structure and syntactic operations involved. Using psycholinguistic experimentation with preschoolers (n=32) and adult speakers of English (n=32), I show that (a) for adults, the intuitions of linguists can be verified experimentally, (b) by the age of 5, children have knowledge of the core aspects of the logical syntax of number words, (c) in spite of this knowledge, children nevertheless differ from adults in systematic ways, (d) the differences observed between children and adults can be accounted for on the basis of an independently motivated, linguistically-based processing model [Geurts, B. (2003). Quantifying kids. Language Acquisition, 11(4), 197-218]. In doing so, this work ties together research on the acquisition of the number vocabulary with a growing body of work on the development of quantification and sentence processing abilities in young children [Geurts, 2003; Lidz, J., Musolino, J. (2002). Children's command of quantification. Cognition, 84, 113-154; Musolino, J., Lidz, J. (2003). The scope of isomorphism: Turning adults into children. Language Acquisition, 11(4), 277-291; Trueswell, J., Sekerina, I., Hilland, N., Logrip, M. (1999). The kindergarten-path effect: Studying on-line sentence processing in young children. Cognition, 73, 89-134; Noveck, I. (2001). When children are more logical than adults: Experimental investigations of scalar implicature. Cognition, 78, 165-188; Noveck, I., Guelminger, R., Georgieff, N., & Labruyere, N. (2007). What autism can tell us about every. . . not sentences. Journal of Semantics,24(1), 73-90. On a more general level, this work confirms the importance of integrating formal and developmental perspectives [Musolino, 2004], this time by highlighting the explanatory power of linguistically-based models of language acquisition and by showing that the complex structure postulated by linguists has important implications for developmental accounts of the number vocabulary. (shrink)

Several recent papers dealing with Plato's position on the imperfection of the phenomenal world draw heavily on the differences between two kinds of predicates in order to show the following: In the middle dialogues, Plato posits Forms only as referents of what the writers call incomplete predicates. He does not posit Forms as referents for complete predicates. When interpreters ignore the differences between these kinds of predicates, they ascribe too radical a view regarding the imperfection of the phenomenal world to (...) the middle dialogues. The ontology of these dialogues includes sensible particulars which retain their identity over time even though they are continually changing in some respect or other. (shrink)

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O (...) comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type. (shrink)

It has long been debated whether objects are ‘sortally’ individuated. This paper begins by clarifying some of the key terms in play—in particular, ‘sortal’, ‘individuation’, and ‘object’. The term ‘individuation’ is taken to have both a cognitive and a metaphysical sense, in the former denoting the singling out of an object in thought and in the latter a determination relation between entities. ‘Sortalism’ is defined as the doctrine that only as falling under some specific sortal concept can (...) an object be successfully singled out in thought. It is argued that such a view is too strong, but that a weaker one, ‘categorialism’, can be defended, this implying that a thinker cannot successfully single out an object in thought without having at least an implicit grasp of the criterion of identity that the object satisfies. (shrink)

W. Labov's & T. Labov's findings concerning their child grammar acquisition ("Learning the Syntax of Questions" in Recent Advances in the Psychology of Language, Campbell, R. & Smith, P. Eds, New York: Plenum Press, 1978) are interpreted in terms of different semantics of why & other wh-questions. Z. Dubiel.

Individuality is an important concept in biology, yet there are many non-equivalent criteria of individuality expressed in different kinds of biological individuals. This article evaluates these different kinds in terms of their capacity to support explanatory generalizations over the systems they individuate. Viewing the problem of individuality from this perspective promotes a splitting strategy in which different kinds make different epistemic trade-offs that suit them for different explanatory roles. I argue that evolutionary individuals, interpreted as forming a functional kind, (...) face difficulties of individuation and explanatory power that are mitigated by relying on more structurally based properties and non-evolutionary kinds. 1Introduction2Kinds of Biological Individuals3Evolutionary Individuals and Functional Kinds4Evolutionary versus Non-evolutionary Kinds of Individuals 4.1Physiological individuality4.2Ecological individuality4.3Developmental individuality5Conclusion. (shrink)

We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' (...) to a binding site in the term, where they are bound); or as functions (since they often, though not always, represent `an unknown'). None of these models is perfect. In every case for the models above, problems arise when trying to use them as a basis for a fully formal mechanical treatment of formal language. The problems are practical—but their underlying cause may be mathematical. The issue is not whether formal syntax exists, since clearly it does, so much as what kind of mathematical structure it is. To illustrate this point by a parody, logical derivations can be modelled using a Gödel encoding (i.e., injected into the natural numbers). It would be false to conclude from this that proof-theory is a branch of number theory and can be understood in terms of, say, Peano's axioms. Similarly, as it turns out, it is false to conclude from the fact that variables can be encoded e.g., as numbers, that the theory of syntax-with-binding can be understood in terms of the theory of syntax-without-binding, plus the theory of numbers (or, taking this to a logical extreme, purely in terms of the theory of numbers). It cannot; something else is going on. What that something else is, has not yet been fully understood. In nominal techniques, variables are an instance of names, and names are data. We model names using urelemente with properties that, pleasingly enough, turn out to have been investigated by Fraenkel and Mostowski in the first half of the 20th century for a completely different purpose than modelling formal language. What makes this model really interesting is that it gives names distinctive properties which can be related to useful logic and programming principles for formal syntax. Since the initial publications, advances in the mathematics and presentation have been introduced piecemeal in the literature. This paper provides in a single accessible document an updated development of the foundations of nominal techniques. This gives the reader easy access to updated results and new proofs which they would otherwise have to search across two or more papers to find, and full proofs that in other publications may have been elided. We also include some new material not appearing elsewhere. (shrink)

In the recent literature of the philosophy of science, much space has been given to the problem of analyzing theories of the deductive and natural sciences in a way which makes explicit some of the syntactic and semantic features which seem to be implicitly present in their structures. This pa- per is concerned with the same problem; however, some other problems of syntax and semantics are touched upon along the way. After some prelim- inaries, a very general method of (...) constructing symbolic languages is intro- duced. The resulting languages are interpreted in either empty or non- empty sets and so in a way which permits them to contain terms which stand for nothing at all and an existence predicate which is not applicable to all terms. Also, certain variable binders are interpreted in a way which leaves open the possibility of interpreting them modally and a semantic operation of degree of truth for arbitrary formulas is introduced. An axiomless logic commensurate with a semantics of this kind and so one which contains a new treatment of definite descriptions is then constructed and shown to be both sound and semantically complete. Finally, theories and various concepts pertaining to theories are defined on the basis of this syntax and semantics. Among the concepts are operations which assign degrees of confirmation, explanatory powers, degrees of deductive simplic- ity, and degrees of adequacy to theories, relations and concreteness and abstractness for expressions, a relation of significance for theories, and operations which assign denotations and meanings to expressions. (shrink)

In a recent article, Harold Noonan argues that application conditions and criteria of identity are not distinct from one another. This seems to threaten the standard approach to distinguishing sortals from adjectival terms. I propose that his observation, while correct, does not have this consequence. I present a simple scheme for distinguishing sortals from adjectival terms. I also propose an amended version of the standard canonical form of criteria of identity.

The assumption that it is possible to distinguish pure syntax from any semantic interpretation is common to contemporary extensionalist approaches to philosophy of language, mind, cognitive science, and artificial intelligence. The origin of the term 'pure syntax' is traced to Carnap's distinction between pure and applied syntax and semantics, and to formalist analyses of mathematical systems as uninterpreted token manipulating games. It is argued in opposition to this trend that syntax can never be purified entirely of (...) semantics, that there can be no such thing as meaningless syntactical tokens or uninterpreted symbols, but that tokens must always betoken and symbols always symbolize something. The implications of the myth of pure syntax in rule-structured and connectionist artificial intelligence, semantic network processing, and their philosophical-psychological rationales, are explored. The fact that rule-structured artificial intelligence in principle can simulate any connectionist model, and that rule-structured artificial intelligence presupposes the myth of pure syntax links the myth to traditional approaches and new paradigms in cognitive engineering. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely (...) speaking) is not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

Like '&', '=' is no term; it represents no extrasentential property. It marks an atomic, nonpredicative, declarative structure, sentences true solely by codesignation. Identity (its necessity and total reflexivity, its substitution rule, its metaphysical vacuity) is the objectual face of codesignation. The syntax demands pure reference, without predicative import for the asserted fact. 'Twain is Clemens' is about Twain, but nothing is predicated of him. Its informational value is in its 'metailed' semantic content: the fact of codesignation (that 'Twain' (...) names Clemens) that explains what fact it asserts and why it is necessary. Critiques of concepts of rigidity and elimination of singular terms result. (shrink)

Manfred Eigen employs the terms language and communication to explain key recombination processes of DNA as well as to explain the self-organization of human language and communication: Life processes as well as language and communication processes are governed by the logic of a molecular syntax, which is the exact depiction of a principally formalizable reality. The author of the present contribution demonstrates that this view of Manfred Eigen’s cannot be sufficiently substantiated and that it must be supplemented by (...) an approach based on linguistic pragmatics. (shrink)

Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formulae and a new derivation of the corresponding result in clone theory, viz. the syntactic description of $\operatorname{Inv(Pol}(R))$ for a given set R of finitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the (...) form of an algorithm. It shows, in the special case of a purely relational type, that duality-theoretic entailment is describable in terms of five constructs, namely trivial relations, intersection, repetition removal, product, and retractive projection. All except the last are concrete, in the sense that they are described by a quantifier-free formula. It is proved that if the finite algebra $\underline{M}$ generates a congruence-distributive variety and all subalgebras of $\underline{M}$ are subdirectly irreducible, then concrete constructs suffice to describe entailment. The concept of entailment appropriate to strong dualities is also introduced, and described in terms of coordinate projections, restriction of domains, and composition of partial functions. (shrink)

The only obligatory temporal expression in English is tense, yet Hans Reichenbach (1947) has argued convincingly that the simplest sentence is understood in terms of three temporal notions. Additional possibilities for a simple sentence are limited: English sentences have one time adverbial each. It is not immediately clear how to resolve these matters, that is, how (if at all) Reichenbach's account can be reconciled with the facts of English. This paper attempts to show that they can be reconciled, and (...) presents an analysis of temporal specification that is based directly on Reichenbach's account.Part I is devoted to a study of the way the three times—speech time, reference time, event time—are realized and interpreted. The relevant syntactic structures and their interaction and interpretation are examined in detail. Part II discusses how a grammar should deal with time specification, and proposes a set of interpretive rules. The study offers an analysis of simple sentences, sentences with complements, and habitual sentences. It is shown that tense and adverbials function differently, depending on the structure in which they appear. The temporal system is relational: the orientation and values of temporal expressions are not fixed, but their relational values are consistent. This consistency allows the statement of principles of interpretation. (shrink)

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. (shrink)

Carnap and Wittgenstein were always far apart on issues of fundamental importance, even on questions where one might have supposed them to be close. Specifically, I will try to show that beneath what at first sight could appear to be a philosophical difference over a mundane question regarding the nature of the propositions of logic, in fact exemplified a chasm between Wittgenstein’s and Carnap’s understanding of our relation to language and the world. After first laying out Carnap’s own understanding of (...) his difference between himself and Wittgenstein on the nature of tautology, I explicate Wittgenstein’s rejection of what would soon become Carnap’s metalogical stance in The Logical Syntax of Language. I do this in terms of Wittgenstein’s reception of Frege, the significance for Wittgenstein of the sign/symbol distinction, and his views of ordinary language and skepticism already at work in the Tractatus. I point out a connection between Heidegger and Wittgenstein on ordinary language that distinguishes them both from the dominant traditions in analytic philosophy of language and from much contemporary post-modernist views of language. Finally I bring out what was at stake personally and culturally for Wittgenstein in his difference from Carnap on logical syntax. (shrink)

The discrepancy between syntax and semantics is a painstaking issue that hinders a better comprehension of the underlying neuronal processes in the human brain. In order to tackle the issue, we at first describe a striking correlation between Wittgenstein's Tractatus, that assesses the syntactic relationships between language and world, and Perlovsky's joint language-cognitive computational model, that assesses the semantic relationships between emotions and “knowledge instinct”. Once established a correlation between a purely logical approach to the language and computable psychological (...) activities, we aim to find the neural correlates of syntax and semantics in the human brain. Starting from topological arguments, we suggest that the semantic properties of a proposition are processed in higher brain's functional dimensions than the syntactic ones. In a fully reversible process, the syntactic elements embedded in Broca's area project into multiple scattered semantic cortical zones. The presence of higher functional dimensions gives rise to the increase in informational content that takes place in semantic expressions. Therefore, diverse features of human language and cognitive world can be assessed in terms of both the logic armor described by the Tractatus, and the neurocomputational techniques at hand. One of our motivations is to build a neuro-computational framework able to provide a feasible explanation for brain's semantic processing, in preparation for novel computers with nodes built into higher dimensions. (shrink)

Contemporary metaphysics is dominated by the view that every object belongs to a kind permanently in the sense that it cannot cease to belong to that kind without thereby ceasing to exist. For example, some philosophers think that a person is destroyed if they cease to be a person, a statue is destroyed if it ceases to be a statue, and so on. I believe that this standard view is false. Being a person, or a statue, or etc., is like (...) being a child: just as I did not cease to exist when I ceased to be a child, so people and statues need not cease to exist when they cease to be people and statues. Borrowing a term from Daniel Korman (who uses it in a similar but perhaps not identical way), I call this view phasalism because it entails that the kind-properties which ordinary objects instantiate are phase sortal properties, i.e., kind-properties that an object can instantiate for a temporary phase of its career. This dissertation is a partial defense of phasalism. I develop a phasalist metaphysics in detail, highlighting its virtues and rebutting objections along the way. After some stage-setting (Chapter 1), I defend a phasalist criterion of identity over time for ordinary objects (Chapter 2), as well as a phasalist account of the role that sortal properties play in the identity over time of ordinary objects (Chapter 3). Then I defend a phasalist-friendly approach to the identity over time of lumps, hunks, pieces, etc. of matter (Chapter 4). The material in these chapters amounts to a phasalist solution to certain material coincidence puzzles, such as the puzzle of the statue and the piece of clay. I go on to show that familiar puzzles about undetached parts (Chapter 5) and fission (Chapter 6) can be solved within the confines of my phasalist metaphysics as well. (shrink)

Linear Syntax makes a case for a critical reassessment of the wide-spread view that syntax can be reduced to tree structures. It argues that a crucial part of the description of German clausal syntax should instead be based on concepts that are defined in terms of linear order. By connecting the descriptive tools of modern phrase-structure grammar with traditional descriptive scholarship, Andreas Kathol offers a new perspective on many long-standing problems in syntactic theory.

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. (shrink)

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights from Aristotle's syllogistic, Scholastic (...) logicians, Leibniz, and the 19th century British algebraists. Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory. Fred Sommers is Professor Emeritus, Brandeis University, USA; George Englebretsen is Professor of Philosophy, Bishop's University, Canada. (shrink)

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.

The paper focuses on the difference between event‐conditionals and premise‐conditionals. An event‐conditional contributes to event structure: it modifies the main clause event; a premise‐conditional structures the discourse: it makes manifest a proposition that is the privileged context for the processing of the associated clause. The two types of conditional clauses will be shown to differ both in terms of their ‘external syntax’ and in terms of their ‘internal syntax’. The peripheral structure of event conditionals will be (...) shown to lack the functional head Force, which encodes illocutionary force. Event conditionals are merged inside the IP of the matrix clause. Premise‐conditionals contain the head Force and they are merged outside the associated CP. (shrink)

The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic (...) data structures, pairs of terms syntax, semantics for example. These sequences then combine with the help of simple generalizations of the usual abstraction and application operations. This theory, which I call Lambda Grammars and which is closely related to the independently formulated theory of Abstract Categorial Grammars (de Groote, 2001; de Groote, 2002), in fact is an implementation of Curry’s ideas: the level of tectogrammar is encoded by the sequences of lambda-terms and their ways of combination, while the syntactic terms in those sequences constitute the phenogrammatical level. In de Groote’s formulation of the theory, tectogrammar is the level of abstract terms, while phenogrammar is the level of object terms. (shrink)

Some philosophers believe that the doctrine that individuals have (nominal) essences is supported by arguments designed to show that proper names have senses. Three such arguments are extracted from recent pieces of philosophy: one from the absurdity of bare particulars, A second from the necessary conditions for identifying bearers of proper names, And a third from the ability to replace proper names in discourse with the help of sortal terms. All three arguments are rejected upon examination. The bearing (...) this rejection has for our conception of how we identify particulars through time is briefly discussed. Finally, An attempt to revive this sort of essentialism vis-A-Vis semantic categories is criticized. (shrink)

This paper is an informal presentation of the ideas presented formally in ”Relative-Sameness Counterpart Theory”. Relative-sameness relations -- such as being the same person as -- are like David Lewis’s “counterpart” relations in the following respects: (i) they may hold over time or across worlds between objects that aren’t cross-time or cross-world identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different contexts. They differ from his counterpart relations, however, (...) in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis’s Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). The use of sameness as opposed to similarity relations in the analysis of de-re temporal and modal predication renders the resulting truth conditions as statable in terms that proponents of Kripke’s identity-based analysis can accept. (shrink)

‘Second substances’ are Aristotle’s species and genera that reveal the general nature of a thing. Sortals correspond to the most specific, least abstract of these, normally thought of as ‘the’ kind to which a thing belongs. I argue against a common view that artifact terms such as ‘clock’ or ‘pen’ are suitable as sortals and for their being regarded as more like genera. If we can individuate clocks and pens as we do trees and rocks, by a combination of (...) sortal plus ostension, then we must use more specific sortals which indicate the structures by virtue of which the objects perform the functions of clocks or pens. Functions by themselves do not supply the identity conditions of sortals. Similar reasoning supports Wiggins’ view that ‘the kind’ to which we belong is our biological species, not the purely functional kind of being a person. (shrink)