“I am not guilty” vs “I am innocent”: Successful negation may depend on the schema used for its encoding

Negations (e.g., “Jim is not guilty”) are part of our daily language and communication. Linguistic and non-linguistic negations can occur when receivers counter-argue what communicators are saying, when hypotheses are disconfirmed, or through negative cognitive responses and many other social interactive processes. Our study explores how negations are encoded by considering the predictions of two theoretical models. According to the fusion model, the core of a negated message and the negation marker are integrated into one meaningful unit. Thus, Jim in the example might be encoded within the schema “innocence.” According to the schema-plus-tag model, a negated message is represented as a core supposition and a negation tag, allowing for dissociation of the two at a later point in time. We compare the two models by examining the nature of inferences that are facilitated by negations. Our results show that the existence of a schema that accommodates the meaning of the original negation is critical in determining how a negation will be encoded. When such a schema is not readily available, processing a negated message facilitates negation-incongruent associations, in line with predictions of the schema-plus-tag model. This model is also supported by analyses of respondents’ memory. We discuss implications of these findings for the communication of negated information, for discounting theories, and for the assessment of the truth of incoming information.     

Subminimal Negation on the Australian Plan

Journal of Philosophical Logic - Frame semantics for negation on the Australian Plan accommodates many different negations, but it falls short on accommodating subminimal negation when the language...     

Impact of negation salience and cognitive resources on negation during attitude formation

Because of the increased cognitive resources required to process negations, past research has shown that explicit attitude measures are more sensitive to negations than implicit attitude measures. The current work demonstrated that the differential impact of negations on implicit and explicit attitude measures was moderated by (a) the extent to which the negation was made salient and (b) the amount of cognitive resources available during attitude formation. When negations were less visually salient, explicit but not implicit attitude measures reflected the intended valence of the negations. When negations were more visually salient, both explicit and implicit attitude measures reflected the intended valence of the negations, but only when perceivers had ample cognitive resources during encoding. Competing models of negation processing, schema-plus-tag and fusion, were examined to determine how negation salience impacts the processing of negations.     

Hegel's Glutty Negation

Some authors have claimed that Hegel's ‘determinate negation’ should be distinguished from ‘logical’ or ‘formal’ negation, that is, from a view of negation as a contradictory forming operator. In contrast, I argue that dialectical determinate negation involves a view of negation as a contradictory forming operator, and can therefore count as formal negation in every respect. However, as it is clear in contemporary glutty semantics of negation, one may distinguish between different accounts of the relationship between negation, contradiction and content. I suggest that, differently from classical negation, and as glutty negation, dialectical negation has partial content.     

Existence,Negation, and Abstraction in the Neoplatonic Hierarchy 1

The paper is a study of the logic of existence, negation, and order in the Neoplatonic tradition. The central idea is that Neoplatonists assume a logic in which the existence predicate is a comparative adjective and in which monadic predicates function as scalar adjectives that nest the background order. Various scalar predicate negations are then identifiable with various Neoplatonic negations, including a privative negation appropriate for the lower orders of reality and a hyper-negation appropriate for the higher. Reversion to the One can then be explained as the logical inference of hyper-negations from mundane knowledge. Part I develops the relevant linguistic and logical theory, and Part II defends Wolfson and the scalar interpretation against the more traditional Aristotelian understanding of Whittaker and others of reversion as intensional abstraction     

Proclus and the Neoplatonic Syllogistic

An investigation of Proclus' logic of the syllogistic and of negations in the Elements of Theology, On the Parmenides, and Platonic Theology. It is shown that Proclus employs interpretations over a linear semantic structure with operators for scalar negations (hypernegation/alpha-intensivum and privative negation). A natural deduction system for scalar negations and the classical syllogistic (as reconstructed by Corcoran and Smiley) is shown to be sound and complete for the non-Boolean linear structures. It is explained how Proclus' syllogistic presupposes converting the tree of genera and species from Plato's diairesis into the Neoplatonic linear hierarchy of Being by use of scalar hyper and privative negations.     

Matching bias and set sizes: A discussion of Yama (2001)

Yama (2001) has presented an ingenious series of experiments in which he attempts to separate two accounts in the literature of the cause of “matching bias” in conditional reasoning. One account is that the bias arises from the way in which people process negations and the other is that it is due to the larger set sizes associated with negative propositions, rather than negation per se. Yama's experiments show influences of both negation and set size, from which he concludes that both factors contribute to the matching bias that is normally observed. In this note, it is argued that this conclusion is at odds with other findings in the literature, particularly those investigating implicit negation as the cause of the bias. Introducing explicit negations has been shown to remove matching bias completely and not partially, as Yama's account must predict. A possible reconciliation is proposed in terms of subtle contextual differences introduced by Yama's experiments.     

A brief history of negation

The history of scholarship on negation tracks and illuminates the major developments in the history of metaphysics, philosophy of language, and philosophy of mind, from Parmenides, Plato and Aristotle through Frege, Russell, and Wittgenstein to contemporary formal theorists. Our perspective focuses on the catalytic role played by the 20th century philosopher of language Paul Grice, whose views on negation serve as a fulcrum for his attempt to bridge the (neo-)Traditionalist and Formalist traditions in logical thought. Grice's remarks on negation and speaker meaning and the elaboration of his ideas by subsequent neo-Griceans are summarized and situated within a broader picture of the role of contradictory and contrary negation in the frameworks of Aristotelians, Medievals, early modern schoolmaster-logicians, 19th and early 20th century neo-Idealists and Formalists, Oxford ordinary-language analytics, practitioners of classical and non-classical logics, and a range of other philosophers and linguists. Particular attention is paid to the relations between negation and the other operators of propositional and predicate calculus. Implications for accounts of the semantics and pragmatics of natural language are also pursued and extensive references to related work are provided.     

Internal Negation and the Principles of Non-Contradiction and of Excluded Middle in Aristotle

It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist of an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations.     

Negation in the Context of Gaggle Theory

We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn's kite of different negations can be dealt with in the extensions of this basic logic K_i. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn's original one. K_u is the minimal logic that has a characteristic semantics. We also show that Shramko's falsification logic FL can be incorporated into some extension of this basic logic K_u. Finally, we unite the two basic logics K_i and K_u together to get a negative modal logic K_-, which is dual to the positive modal logic K₊ in [7]. Shramko has suggested an extension of Dunn's kite and also a dual version in [12]. He also suggested combining them into a “united” kite. We give a united semantics for this united kite of negations.     

Heuristic and analytic processes in propositional reasoning with negatives

The authors report 4 studies on heuristic and analytic processes in conditional reasoning with negations and show that a heuristic negative conclusion bias cannot account for the effects observed on problem-solving latencies derived from eye-movement measures (Experiment 1) and a novel mouse-tracking methodology (Experiment 2). A double negation elimination process can account for both the latency and response-frequency effects of a negation in the clause about which an inference is made. It is further shown that other negation effects cannot be explained by an affirmative premise bias proposed in the literature. Experiments 3 and 4 demonstrate that a novel availability hypothesis provides a viable alternative. It is argued that extant analytic theories need to be extended to incorporate a validating search for counter examples and need to specify how pragmatic and comprehension processes influence such a search.     

An experimental approach to language training in second language acquisition: Focus on negation

The effect of negation training in a second language on the expression of negation in the native language was investigated. Four-year-old children from bilingual (Spanish/English) homes who showed no expressive or receptive ability in Spanish negation and were either proficient or nonproficient in English negation received Spanish negation training. Children who were proficient in English negation maintained correct responses in English and showed increased correct responses in Spanish following simultaneous training in both languages or in Spanish alone. Children who were nonproficient in English negation demonstrated a decrease in correct English responses following training in Spanish alone; however, children who received training in English and Spanish simultaneously showed increases in correct responses in both languages. These findings suggest that language training programs with children learning a second language should consider the relationship of the two language training conditions (simultaneous vs. independent) with the child's level of native language proficiency.     

The Role of Negation in Conditional Inference

This paper addresses the issue of how negative components affect people's ability to draw conditional inferences. The study was motivated by an attempt to resolve a difficulty for the mental models theory of Johnson-Laird and Byrne, whose account of matching bias in the selection task is apparently inconsistent with Johnson-Laird's explanation of the double negation effects in conditional inference reported by Evans, Clibbens, and Rood (1995). Two experiments are reported, which investigate frequencies of conditional inferences with task presentation similar to that of the selection task in two respects: the presence of a picture of four cards and the use of implicit negations in the premises. The latter variable was shown to be critical and demonstrated a new phenomenon: Conditional inferences of all kinds are substantially suppressed when based on implicitly negative premises. This phenomenon was shown to operate independently of and in addition to the double negation effect. A third experiment showed that the implicit negation effect could be extended to the paradigm in which people are asked to produce their own conclusions. It is argued that these two effects can be explained within either the mental models theory or the inference rule theory, of propositional reasoning, but that each will require some revision in order to offer a convincing account.     

Planning what not to eat: ironic effects of implementation intentions negating unhealthy habits

The present studies tested the effectiveness of implementation intentions with an "if [situation], then not [habitual response]" structure. Based on ironic process theory and the literature on the processing of negations, it was expected that these "negation implementation intentions" would, ironically, strengthen the habit (situation-response association) one aims to break. In line with the hypotheses, forming negation implementation intentions resulted in cognitive ironic rebound effects as well as behavioral ironic rebound effects compared to an intention only condition or a replacement implementation intention. Additionally, it was found that negation implementation intentions are most likely to result in ironic rebound effects when the habit to be negated is strong. Although implementation intentions are generally highly effective in facilitating behavior change even when this involves breaking unwanted habits, the present research suggests that they are ineffective when they have a negating structure.     

Maltreated Children Use More Grammatical Negations

Many studies reveal a strong impact of childhood maltreatment on language development, mainly resulting in shorter utterances, less rich vocabulary, or a delay in grammatical complexity. However, different theories suggest the possibility for resilience—a positive adaptation to an otherwise adverse environment—in children who experienced childhood maltreatment. Here, we investigated different measures for language development in spontaneous speech, examining whether childhood maltreatment leads to a language deficit only or whether it can also result in differences in language use due to a possible adaptation to a toxic environment. We compared spontaneous speech during therapeutic peer-play sessions of 32 maltreated and 32 non-maltreated children from the same preschool and equivalent in gender, age (2 to 5 years), home neighborhood, ethnicity, and family income. Maltreatment status was reported by formal child protection reports, and corroborated by independent social service reports. We investigated general language sophistication (i.e., vocabulary, talkativeness, mean length of utterance), as well as grammatical development (i.e., use of plurals, tense, grammatical negations). We found that maltreated and non-maltreated children showed similar sophistication across all linguistic measures, except for the use of grammatical negations. Maltreated children used twice as many grammatical negations as non-maltreated children. The use of this highly complex grammatical structure shows an advanced linguistic skill, which shows that childhood maltreatment does not necessarily lead to a language deficit. The result might indicate the development of a negativity bias in the structure of spontaneous language due to an adaptation to their experiences.     

At the boundaries of automaticity: negation as reflective operation

The present research investigated whether automatic social-cognitive skills are based on the same representations and processes as their controlled counterparts. Using the cognitive task of negating valence, the authors demonstrate that enhanced practice in negating the valence of a stimulus can lead to changes in the underlying associative representation. However, procedural, rule-based components of negations were generally unaffected by practice (Experiments 1-3). Moreover, negations of evaluative stimuli did not influence automatic evaluative responses to these stimuli, unless the negation was included in the associative representation of a stimulus (Experiments 4-6). These results suggest that some practice-related skill improvements are limited to conditions in which a general procedure can be substituted by the retrieval of results of previous applications from associative memory. Implications for research on automaticity and social cognition are discussed.     

There is More to Negation than Modality

There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto (Mind, 124(495), 761–793, 2015) defends at length in a recent paper. According to one such modal account, the negation of a sentence is true at a world x just in case all the worlds at which the sentence is true are incompatible with x. Incompatibility is taken to be the key notion in the account, and what minimal properties a negation has comes down to which minimal conditions incompatibility satisfies. Our aims in this paper are twofold. First, we wish to point out problems for the modal account that make us question its tenability on a fundamental level. Second, in its place we propose an alternative, non-modal, account of negation as a contradictory-forming operator that we argue is superior to, and more natural than, the modal account.     

Moral expressivism and sentential negation

This paper advances three necessary conditions on a successful account of sentential negation. First, the ability to explain the constancy of sentential meaning across negated and unnegated contexts (the Fregean Condition). Second, the ability to explain why sentences and their negations are inconsistent, and inconsistent in virtue of the meaning of negation (the Semantic Condition). Third, the ability of the account to generalize regardless of the topic of the negated sentence (the Generality Condition). The paper discusses three accounts of negation available to moral expressivists. The first—the dominant commitment account—fails to meet the Fregean Condition. The two remaining accounts—commitment semantics and the expression account—satisfy all three conditions. A recent argument that the dominant commitment account is the only option available to expressivists is considered and rejected.