Citations of:
What are logical notions?
History and Philosophy of Logic 7 (2):143154 (1986)
Add citations
You must login to add citations.


The aim of this paper is to provide a dynamic interpretation of Kant’s logical hylomorphism. Firstly, various types of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate Kant’s constitutivity thesis about logic. Finally, I focus on the design of logical norms as specific kinds of artefacts. 

In a recent discussion article in this journal, Gila Sher responds to some of my criticisms of her work on what she calls the formalstructural account of logical consequence. In the present paper I reply and attempt to advance the discussion in a constructive way. Unfortunately, Sher seems to have not fully understood my 1997. Several of the defenses she mounts in her 2001 are aimed at views I do not hold and did not advance in my 1997. Most prominent (...) 

Starting from certain metalogical results, I argue that firstorder logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that firstorder logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach to these (...) 

The interactivist model has explored a number of consequences of process metaphysics. These include reversals of some fundamental metaphysical assumptions dominant since the ancient Greeks, and multiple further consequences throughout the metaphysics of the world, minds, and persons. This article surveys some of these consequences, ranging from issues regarding entities and supervenience to the emergence of normative phenomena such as representation, rationality, persons, and ethics. 

List and Pettit have stated an impossibility theorem about the aggregation of individual opinion states. Building on recent work on the lottery paradox, this paper offers a variation on that result. The present result places different constraints on the voting agenda and the domain of profiles, but it covers a larger class of voting rules, which need not satisfy the propositionwise independence of votes. 

Alfred Tarski's (1936) semantic account of the logical properties (logical consequence, logical truth and logical consistency) makes essential appeal to a distinction between logical and nonlogical terms. John Etchemendy (1990) has recently argued that Tarski's account is inadequate for quite a number of different reasons. Among them is a brief argument which purports to show that Tarski's reliance on the distinction between logical and nonlogical terms is in principle mistaken. According to Etchemendy, there are very simple (even first order) languages (...) 

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...) 

This essay addresses the collapse/incoherence problem for normative frameworks that contain both fundamental values and rules for promoting those values. The problem is that in some cases, we would bring about more of the fundamental value by violating the framework’s rules than by following them. In such cases, if the framework requires us to follow the rules anyway, then it appears to be incoherent; but if it allows us to make exceptions to the rules, then the framework “collapses” into one (...) 

The relation of global supervenience is widely appealed to in philosophy. In slogan form, it is explained as follows: a class of properties A supervenes on a class of properties B if no two worlds differ in the distribution of Aproperties without differing in the distribution of Bproperties. It turns out, though, that there are several ways to cash out that slogan. Three different proposals have been discussed in the literature. In this paper, I argue that none of them is (...) 

In this dissertation, I argue that we should be pluralists about truth and in turn, eliminativists about the property Truth. Traditional deflationists were right to suspect that there is no such property as Truth. Yet there is a plurality of pluralities of properties which enjoy defining features that Truth would have, were it to exist. So although, in this sense, truth is plural, Truth is nonexistent. The resulting account of truth is indebted to deflationism as the provenance of the suspicion (...) 

Philosophers are divided on whether the proof or truththeoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truthbased approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and prooftheoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, strong modal force, generality, (...) 

It's often said that according to deflationary theories of truth, truth is not a ‘substantial’ property. While this is a fine slogan, it is far from transparent what deflationists mean (or ought to mean) in saying that truth is ‘insubstantial’. Focusing so intently upon the concept of truth and the word ‘true’, I argue, deflationists and their critics have been insufficiently attentive to a host of metaphysical complexities that arise for deflationists in connection with the property of truth. My aim (...) 

C. I. Lewis (I883I964) was the first major figure in history and philosophy of logic—a field that has come to be recognized as a separate specialty after years of work by Ivor GrattanGuinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...) 

Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical (...) 

In the literature on supervaluationism, a central source of concern has been the acceptability, or otherwise, of its alleged logical revisionism. I attack the presupposition of this debate: arguing that when properly construed, there is no sense in which supervaluational consequence is revisionary. I provide new considerations supporting the claim that the supervaluational consequence should be characterized in a ‘global’ way. But pace Williamson (1994) and Keefe (2000), I argue that supervaluationism does not give rise to counterexamples to familiar inferencepatterns (...) 



It is widely believed that some puzzling and provocative remarks that Frege makes in his late writings indicate he rejected independence arguments in geometry, particularly arguments for the independence of the parallels axiom. I show that this is mistaken: Frege distinguished two approaches to independence arguments and his puzzling remarks apply only to one of them. Not only did Frege not reject independence arguments across the board, but also he had an interesting positive proposal about the logical structure of correct (...) 

The relevance of any logical analysis lies in its ability to solve paradoxes and trace conceptual troubles back; with this respect, the task of epistemic logic is to handle paradoxes in connection with the concept of knowledge. Epistemic logic is currently introduced as the logical analysis of crucial concepts within epistemology, namely: knowledge, belief, truth, and justification. An alternative approach will be advanced here in order to enlighten such a discourse, as centred upon the word assertion and displayed in terms (...) 

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...) 

Content words are generally connected: there are no gaps in their denotations; no noun means ‘table or shoe’ or ‘animal or house’. We explore a formulation of connectedness which is applicable to content and logical words alike, and which compares well with the classic notion of monotonicity for quantifiers. On a first inspection, logical words satisfy this generalized version of the connectedness property at least as well as content words do — that is, both in terms of what may be (...) 

The aim of this paper is to provide a dynamic interpretation of Kant’s logical hylomorphism. Firstly, various types of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate Kant’s constitutivity thesis about logic. Finally, I focus on the design of logical norms as specific kinds of artefacts. 

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11page 1936 Tarski consequencedefinition paper is based on a monistic fixeduniverse framework?like Begriffsschrift and Principia Mathematica. Monistic fixeduniverse frameworks, common in preWWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multipleuniverse framework?like the 1931 Gödel incompleteness paper. A pluralistic multipleuniverse framework recognizes multiple (...) 

A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. These are 'natural' concepts of validity and completeness, which were, however, in the course of the history of modern logic, stealthily replaced by their formal descendants: formal validity and completeness. A formula is formally valid iff it is true under all interpretations in all universes; and an axiomatic system is called (...) 

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation. 

Informally, structural properties of mathematical objects are usually characterized in one of two ways: either as properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. We present two formal explications corresponding to these two informal characterizations of structural properties. Based on this, we discuss the relation between the two explications. As will be shown, the two characterizations do not determine the same class of mathematical properties. (...) 



The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance (...) 

I characterize the deductivist ideal of justification and, following to a great extent Toulmin’s work The Uses of Argument, I try to explain why this ideal is erroneous. Then I offer an alternative model of justification capable of making our claims to knowledge about substantial matters sound and reasonable. This model of justification will be based on a conception of justification as the result of good argumentation, and on a model of argumentation which is a pragmatic linguistic reconstruction of Toulmin’s (...) 

Here I revisit Bolzano's criticisms of Kant on the nature of logic. I argue that while Bolzano is correct in taking Kant to conceive of the traditional logic as a science of the activity of thinking rather than the content of thought, he is wrong to charge Kant with a failure to identify and examine this content itself within logic as such. This neglects Kant's own insistence that traditional logic does not exhaust logic as such, since it must be supplemented (...) 

Branching quantifiers were first introduced by L. Henkin in his 1959 paper ‘Some Remarks on Infmitely Long Formulas’. By ‘branching quantifiers’ Henkin meant a new, nonlinearly structured quantiiierprefix whose discovery was triggered by the problem of interpreting infinitistic formulas of a certain form} The branching (or partiallyordered) quantifierprefix is, however, not essentially infinitistic, and the issues it raises have largely been discussed in the literature in the context of finitistic logic, as they will be here. Our discussion transcends, however, the (...) 

In the paper the following questions are discussed: What is logical consequence? What are logical constants? What is a logical system? What is logical pluralism? What is logic? In the conclusion, the main tendencies of development of modern logic are pointed out. 

El objetivo de este artículo es investigar diversos resultados limitativos acerca del concepto de validez. En particular, argumento que ninguna teoría lógica de orden superior con semántica estándar puede tener recursos expresivos suficientes como para capturar su propio concepto de validez. Además, muestro que la lógica de la verdad transparente que Hartry Field desarrolló recientemente conduce a resultados limitativos similares. 

Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as he (...) 

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations. 

This paper is concerned with formal solutions to the lottery paradox on which high probability defeasibly warrants acceptance. It considers some recently proposed solutions of this type and presents an argument showing that these solutions are trivial in that they boil down to the claim that perfect probability is sufficient for rational acceptability. The argument is then generalized, showing that a broad class of similar solutions faces the same problem. An argument against some formal solutions to the lottery paradox The (...) 

The paper offers a new analysis of the difficulties involved in the construction of a general and substantive correspondence theory of truth and delineates a solution to these difficulties in the form of a new methodology. The central argument is inspired by Kant, and the proposed methodology is explained and justified both in general philosophical terms and by reference to a particular variant of Tarski's theory. The paper begins with general considerations on truth and correspondence and concludes with a brief (...) 

Ontology is the study of what there is, what kinds of things make up reality. Ontology seems to be a very difficult, rather speculative discipline. However, it is trivial to conclude that there are properties, propositions and numbers, starting from only necessarily true or analytic premises. This gives rise to a puzzle about how hard ontological questions are, and relates to a puzzle about how important they are. And it produces the ontologyobjectivity dilemma: either (certain) ontological questions can be trivially (...) 

I argue that we can and should extend Tarski's modeltheoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles. 

One logic or many? I say—many. Or rather, I say there is one logic for each way of specifying the class of all possible circumstances, or models, i.e., all ways of interpreting a given language. But because there is no unique way of doing this, I say there is no unique logic except in a relative sense. Indeed, given any two competing logical theories T1 and T2 (in the same language) one could always consider their common core, T, and settle (...) 

In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. This raises two (...) 

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) 

This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two inﬂuential accounts of consequence, the modeltheoretic and the prooftheoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We brieﬂy discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections (...) 

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the (...) 

This thesis aims to develop a psychologically plausible account of concepts by integrating key insights from philosophy (on the metaphysical basis for concept possession) and psychology (on the mechanisms underlying concept acquisition). I adopt an approach known as informational atomism, developed by Jerry Fodor. Informational atomism is the conjunction of two theses: (i) informational semantics, according to which conceptual content is constituted exhaustively by nomological mind–world relations; and (ii) conceptual atomism, according to which (lexical) concepts have no internal structure. I (...) 

In a first section, we discuss Quine’s claim according to which identity is a logical notion. We point out that Quine mixes up various types of identities: trivial identity, Leibniz identity, etc.; and this leads him to commit several mistakes. In a second section, we review Quine’s criticisms to various philosophers, who according to him made confusion between names and objects in defining identity. We show that in fact only Korzybski can be accused of such confusion. In a third section, (...) 



In this paper I examine a cluster of concepts relevant to the methodology of truth theories: 'informative definition', 'recursive method', 'semantic structure', 'logical form', 'compositionality', etc. The interrelations between these concepts, I will try to show, are more intricate and multidimensional than commonly assumed. 

Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant. 

Italian translation of "On Logical Relativity" (2002), by Luca Morena. 