Workshop on Negation and Denial
Faculty of Letters, University of Lisbon
7, 8 July 2008
Do I contradict you if I reject what you have just said? Can I coherently reject both a sentence and its negation? Is there any difference between denying an uttered sentence and asserting the negation of that sentence? The concept of negation is central for understanding core problems in philosophical logic and philosophy of language. How one answers the questions above depends at least on which logical principles one thinks are correct, on whether one thinks the principle of bivalence holds or not, on what negation means, and on what kind of speech act rejection (or denial) is, if any.
Poster
7 July
10:30
Terence Parsons (UCLA, University of California, Los Angeles)
Exclusion Negation
Choice negation is a connective that converts a true sentence into a false one, a false one into a true one, and a truth-valueless sentence with a truth-valueless one. Exclusion negation is a connective that converts a true sentence into false one, and any other sentence into a true one. Popular solutions of the Liar Paradox classify the liar sentence as a sentence without truth value. But this idea seems to fail when the liar sentence is reformulated using exclusion negation instead of choice negation. In "Assertion, Denial, and the Liar Paradox," I considered (favorably) the possibility that there might be no such thing as exclusion negation. In Indeterminate Identity, however, I made frequent use of exclusion negation (in the guise of choice negation together with a determinacy connective). My talk will explore how these two approaches might be reconciled, perhaps by replacing the determinacy connective with an intensional determinacy operator. I don't like this idea much, but I can't find a better way to have an overall consistent view.
12:10
Pablo Cobreros (University of Navarra)
Symmetry, Negation and Truth-value Gaps
We can justify the existence of a truth-value gap with a sort of argument based on a symmetry of the justification for a sentence’s truth and the truth of its negation. This paper considers a response of Williamson to one of these arguments connected to vagueness. The paper notes that Williamson’s response rests crucially on a particular understanding of the nature of negation. Williamson’s view is contrasted with the more traditional Aristotelian view on negation. The paper provides some discussion concerning the Aristotelian view.
15:00
Nils Kurbis (University College London)
Can Negation be Defined in Terms of Incompatibility?
Every theory needs primitives. A primitive is a term that is not defined any further, but is used to define others. Thus theories should use primitives that can be expected to be understood by everyone. Negation is a a very fundamental concept. No one has problems grasping it. It is a perfect choice for a primitive. Nonetheless, there have been attempts to define it in terms of allegedly more fundamental concepts. The motivation behind such attempts is to provide a principled basis on which to settle the debate between rival logicians concerning the correct properties of negation. Most prominently, the debate between classicists and intuitionists is largely one about the laws governing negation. If negation is chosen as a primitive, no principled decision can be made. I shall investigate how successful such attempts are. In particular, I shall argue that defining negation in terms of incompatibility fails, because the latter notion is conceptually rather more demanding notion than negation. Besides, the approach fails to decide between classicists and intuitionists. As a matter of fact different incompatibility-theorists come to different conclusions concerning which logic is the right one. Thus quite apart from the conceptual difficulties involved in choosing incompatibility as primitive, in the light of the debate between classicists and intuitionists, the approach does not fare any better than choosing negation as primitive.
17:05
Luca Tranchini (University of Siena)
The Meaning of Negation: A Proposal
A line of thought offering a possible solution to the problem of fixing the meaning of negation by purely proof-theoretical means is presented. The starting points are Tennant's rejection of treating ^ as a propositional constant and his idea of developing a framework in which it is possible to account for both proofs and refutations. We try to link Tennant's ideas with Dummett and Prawitz's suggestions according to which the verificationist theory of meaning has its specular in a falsificationist (or pragmatist) theory of meaning. In so doing light will be shed on Dummett's (1991) claim about the consistency principle. The result is an alternative interpretation of the IØ and EØ rules showing that negation, rather than a connective, is a device which reveals the symmetry between assumptions and conclusions implicit in syntax.
18:25
José Martínez (University of Barcelona)
On the consistency of negations in four-valued generalizations of Kleene logics
First-order language has the fixed-point property when (roughly speaking) a Kripkean truth predicate for the language can be defined. I will present some theorems on (non-quantificational) languages having the fixed-point property. Using those theorems I will discuss the consistency of certain operators of negation in four-valued generalizations of Kleene logics (strong and weak).
8 July
10:30
Ian Rumfitt (Birkbeck College, London)
Negation and Possibilities
What is it for one statement to be a negation of another? I begin by canvassing various sorts of answer, and argue that the best answer will be one which states the relationship between the truth-grounds of a negated statement, and the truth-grounds of the component negand. By a truth-ground of a statement, I mean a possibility in which it is true; by a possibility, I mean a way some things—some things—could have been. I argue for the superiority of this account over a more familiar rival, whereby a statement’s logically relevant meaning is given by the possible worlds in which it is true. Following Dunn and others, I defend an account whereby the truth-grounds of ‘not A’ are those possibilities that are incompatible with every truth-ground of A. I conclude by explaining how disputes over fundamental logical laws involving negation can be understood on the present approach, and how the theory can contribute to a rational resolution of those disputes.
12:10
Gonçalo Santos (IHPST, Université Paris 1 and LanCog, Universidade de Lisboa)
Some Problems With Bilateralism
Michael Dummett and Ian Rumfitt try to explain the sense of a sentence in terms of the use that we make of it. They disagree however in their identification of the necessary conditions for mastering use. Dummett claims that mastering a sentence only presupposes understanding the conditions that allow its assertion, while Rumfitt claims that mastering a sentence not only presupposes understanding the conditions that allow its assertion but also the conditions that allow its rejection. As a consequence of this disagreement, even if both claim that the sense of a logical constant is given by its introduction and elimination rules, the sets of rules favoured by each of them differs.
Dummett argues in favour of the adoption of a unilateral conception of meaning. In particular, he tries to explain the rejection of a sentence as the assertion of its negation. He also claims that the intuitionist rules for the introduction and elimination of negation agree with this conception. Rumfitt tries to justify the adoption of a bilateral conception of meaning, and through it, explain the negation of a sentence as the satisfaction of the conditions for its rejection. He argues that the classical understanding of negation agrees with such a conception and that the adoption of bilateralism provides the classical logician with an answer to a well known intuitionist criticism. We will argue that an objection raised by Dummett causes serious difficulties for the bilateralist conception of meaning.
15:00
Bradley Armour-Garb (Albany University) and James Woodbridge (UNLV)
Negation and Non-Assertoric Denial
A number of philosophers have argued against Frege's equation of (the act of) denial with assertion of negation. They have, instead (and for various reasons), postulated a sui generis (speech) act of denial. Their claim is that we can use this notion to resolve various paradoxes and/or give sense to the logical connectives--in particular, negation. Call such philosophers 'Cancelers' and call the kind of view they offer 'rejectivism' (or: 'bilateral rejectivism'). In this talk, after briefly summarising some of the main features of (bilateral) rejectivism, we critically evaluate the accounts offered by several Cancelers, focusing on the problems facing their various proposals. After raising some objections to the particular views we consider, we provide arguments against the prospect of (bilateral) rejectivism in general.
17:05
Edward Kanterian (Trinity College, Oxford)
Definite Descriptions, Presuppositions and Metalinguistic Negation
It has been claimed that Strawson’s theory of definite descriptions cannot handle contexts determined by so-called metalinguistic negation (Horn 1996, 2001). In such contexts sentences containing an empty description don’t seem to be lacking a truth-value and to be carrying the presupposition predicted by the theory, save on pain of contradiction. I argue that these contexts in fact do not give rise to any contradiction, because metalinguistic negation amounts to a peculiar use of ordinary descriptive negation made fully explicit not in the initial negation sentence, but only in the ensuing corrector sentence, i.e. the actual denial of the presupposition. This account is briefly compared with other treatments of the metalinguistic challenge to the analysis of definite descriptions (e.g. Burton-Roberts 1989, 1990, van der Sandt/Maier 2003).
18:25
Michael Gabbay (King's College London)
Dummett, Rumfitt and Classical Negation
In this paper I discuss how a proof-theoretic treatment of logical constants, in particular negation, leads to the famous requirement that logical inference rules should be in harmony. I consider and reject one method for adapting Dummett's strategy to apply to classical logic, and describe my own alternative. I conclude that with a modi cation to the inference rules for nega- tion, classical logic can be justi ed by a justi cation method along Dummett's lines.
Organization:
Teresa Marques (Barcelona/Lisbon)
Pedro Santos (Algarve/Lisbon)
Sara Bizarro (Lisbon)
Carla Simões (University of Lisbon)
Scientific Committee:
Terence Parsons (UCLA)
Ian Rumfitt (BBK College London)
Manuel García-Carpintero (Barcelona)
José Martinez (Barcelona)
Josep Macià (Barcelona)
Sven Rosenkranz (Barcelona/St Andrews/Berlin)
Pablo Cobreros (Navarra)
Peter Pagin (Stockholm)
Pedro Santos (Algarve/Lisbon)
Sponsors:
Fundação para a Ciência e Tecnologia
Caixa Geral de Depósitos
7, 8 July 2008
Do I contradict you if I reject what you have just said? Can I coherently reject both a sentence and its negation? Is there any difference between denying an uttered sentence and asserting the negation of that sentence? The concept of negation is central for understanding core problems in philosophical logic and philosophy of language. How one answers the questions above depends at least on which logical principles one thinks are correct, on whether one thinks the principle of bivalence holds or not, on what negation means, and on what kind of speech act rejection (or denial) is, if any.
Poster
7 July
10:30
Terence Parsons (UCLA, University of California, Los Angeles)
Exclusion Negation
Choice negation is a connective that converts a true sentence into a false one, a false one into a true one, and a truth-valueless sentence with a truth-valueless one. Exclusion negation is a connective that converts a true sentence into false one, and any other sentence into a true one. Popular solutions of the Liar Paradox classify the liar sentence as a sentence without truth value. But this idea seems to fail when the liar sentence is reformulated using exclusion negation instead of choice negation. In "Assertion, Denial, and the Liar Paradox," I considered (favorably) the possibility that there might be no such thing as exclusion negation. In Indeterminate Identity, however, I made frequent use of exclusion negation (in the guise of choice negation together with a determinacy connective). My talk will explore how these two approaches might be reconciled, perhaps by replacing the determinacy connective with an intensional determinacy operator. I don't like this idea much, but I can't find a better way to have an overall consistent view.
12:10
Pablo Cobreros (University of Navarra)
Symmetry, Negation and Truth-value Gaps
We can justify the existence of a truth-value gap with a sort of argument based on a symmetry of the justification for a sentence’s truth and the truth of its negation. This paper considers a response of Williamson to one of these arguments connected to vagueness. The paper notes that Williamson’s response rests crucially on a particular understanding of the nature of negation. Williamson’s view is contrasted with the more traditional Aristotelian view on negation. The paper provides some discussion concerning the Aristotelian view.
15:00
Nils Kurbis (University College London)
Can Negation be Defined in Terms of Incompatibility?
Every theory needs primitives. A primitive is a term that is not defined any further, but is used to define others. Thus theories should use primitives that can be expected to be understood by everyone. Negation is a a very fundamental concept. No one has problems grasping it. It is a perfect choice for a primitive. Nonetheless, there have been attempts to define it in terms of allegedly more fundamental concepts. The motivation behind such attempts is to provide a principled basis on which to settle the debate between rival logicians concerning the correct properties of negation. Most prominently, the debate between classicists and intuitionists is largely one about the laws governing negation. If negation is chosen as a primitive, no principled decision can be made. I shall investigate how successful such attempts are. In particular, I shall argue that defining negation in terms of incompatibility fails, because the latter notion is conceptually rather more demanding notion than negation. Besides, the approach fails to decide between classicists and intuitionists. As a matter of fact different incompatibility-theorists come to different conclusions concerning which logic is the right one. Thus quite apart from the conceptual difficulties involved in choosing incompatibility as primitive, in the light of the debate between classicists and intuitionists, the approach does not fare any better than choosing negation as primitive.
17:05
Luca Tranchini (University of Siena)
The Meaning of Negation: A Proposal
A line of thought offering a possible solution to the problem of fixing the meaning of negation by purely proof-theoretical means is presented. The starting points are Tennant's rejection of treating ^ as a propositional constant and his idea of developing a framework in which it is possible to account for both proofs and refutations. We try to link Tennant's ideas with Dummett and Prawitz's suggestions according to which the verificationist theory of meaning has its specular in a falsificationist (or pragmatist) theory of meaning. In so doing light will be shed on Dummett's (1991) claim about the consistency principle. The result is an alternative interpretation of the IØ and EØ rules showing that negation, rather than a connective, is a device which reveals the symmetry between assumptions and conclusions implicit in syntax.
18:25
José Martínez (University of Barcelona)
On the consistency of negations in four-valued generalizations of Kleene logics
First-order language has the fixed-point property when (roughly speaking) a Kripkean truth predicate for the language can be defined. I will present some theorems on (non-quantificational) languages having the fixed-point property. Using those theorems I will discuss the consistency of certain operators of negation in four-valued generalizations of Kleene logics (strong and weak).
8 July
10:30
Ian Rumfitt (Birkbeck College, London)
Negation and Possibilities
What is it for one statement to be a negation of another? I begin by canvassing various sorts of answer, and argue that the best answer will be one which states the relationship between the truth-grounds of a negated statement, and the truth-grounds of the component negand. By a truth-ground of a statement, I mean a possibility in which it is true; by a possibility, I mean a way some things—some things—could have been. I argue for the superiority of this account over a more familiar rival, whereby a statement’s logically relevant meaning is given by the possible worlds in which it is true. Following Dunn and others, I defend an account whereby the truth-grounds of ‘not A’ are those possibilities that are incompatible with every truth-ground of A. I conclude by explaining how disputes over fundamental logical laws involving negation can be understood on the present approach, and how the theory can contribute to a rational resolution of those disputes.
12:10
Gonçalo Santos (IHPST, Université Paris 1 and LanCog, Universidade de Lisboa)
Some Problems With Bilateralism
Michael Dummett and Ian Rumfitt try to explain the sense of a sentence in terms of the use that we make of it. They disagree however in their identification of the necessary conditions for mastering use. Dummett claims that mastering a sentence only presupposes understanding the conditions that allow its assertion, while Rumfitt claims that mastering a sentence not only presupposes understanding the conditions that allow its assertion but also the conditions that allow its rejection. As a consequence of this disagreement, even if both claim that the sense of a logical constant is given by its introduction and elimination rules, the sets of rules favoured by each of them differs.
Dummett argues in favour of the adoption of a unilateral conception of meaning. In particular, he tries to explain the rejection of a sentence as the assertion of its negation. He also claims that the intuitionist rules for the introduction and elimination of negation agree with this conception. Rumfitt tries to justify the adoption of a bilateral conception of meaning, and through it, explain the negation of a sentence as the satisfaction of the conditions for its rejection. He argues that the classical understanding of negation agrees with such a conception and that the adoption of bilateralism provides the classical logician with an answer to a well known intuitionist criticism. We will argue that an objection raised by Dummett causes serious difficulties for the bilateralist conception of meaning.
15:00
Bradley Armour-Garb (Albany University) and James Woodbridge (UNLV)
Negation and Non-Assertoric Denial
A number of philosophers have argued against Frege's equation of (the act of) denial with assertion of negation. They have, instead (and for various reasons), postulated a sui generis (speech) act of denial. Their claim is that we can use this notion to resolve various paradoxes and/or give sense to the logical connectives--in particular, negation. Call such philosophers 'Cancelers' and call the kind of view they offer 'rejectivism' (or: 'bilateral rejectivism'). In this talk, after briefly summarising some of the main features of (bilateral) rejectivism, we critically evaluate the accounts offered by several Cancelers, focusing on the problems facing their various proposals. After raising some objections to the particular views we consider, we provide arguments against the prospect of (bilateral) rejectivism in general.
17:05
Edward Kanterian (Trinity College, Oxford)
Definite Descriptions, Presuppositions and Metalinguistic Negation
It has been claimed that Strawson’s theory of definite descriptions cannot handle contexts determined by so-called metalinguistic negation (Horn 1996, 2001). In such contexts sentences containing an empty description don’t seem to be lacking a truth-value and to be carrying the presupposition predicted by the theory, save on pain of contradiction. I argue that these contexts in fact do not give rise to any contradiction, because metalinguistic negation amounts to a peculiar use of ordinary descriptive negation made fully explicit not in the initial negation sentence, but only in the ensuing corrector sentence, i.e. the actual denial of the presupposition. This account is briefly compared with other treatments of the metalinguistic challenge to the analysis of definite descriptions (e.g. Burton-Roberts 1989, 1990, van der Sandt/Maier 2003).
18:25
Michael Gabbay (King's College London)
Dummett, Rumfitt and Classical Negation
In this paper I discuss how a proof-theoretic treatment of logical constants, in particular negation, leads to the famous requirement that logical inference rules should be in harmony. I consider and reject one method for adapting Dummett's strategy to apply to classical logic, and describe my own alternative. I conclude that with a modi cation to the inference rules for nega- tion, classical logic can be justi ed by a justi cation method along Dummett's lines.
Organization:
Teresa Marques (Barcelona/Lisbon)
Pedro Santos (Algarve/Lisbon)
Sara Bizarro (Lisbon)
Carla Simões (University of Lisbon)
Scientific Committee:
Terence Parsons (UCLA)
Ian Rumfitt (BBK College London)
Manuel García-Carpintero (Barcelona)
José Martinez (Barcelona)
Josep Macià (Barcelona)
Sven Rosenkranz (Barcelona/St Andrews/Berlin)
Pablo Cobreros (Navarra)
Peter Pagin (Stockholm)
Pedro Santos (Algarve/Lisbon)
Sponsors:
Fundação para a Ciência e Tecnologia
Caixa Geral de Depósitos
