Conditional Excluded Middle

In this essay I renew the case for Conditional Excluded Middle (CXM) in light of recent developments in the semantics of the subjunctive conditional. I argue that Michael Tooley’s recent backward causation counterexample to the Stalnaker-Lewis comparative world similarity semantics undermines the strongest argument against CXM, and I offer a new, principled argument for the validity of CXM that is in no way undermined by Tooley’s counterexample. Finally, I formulate a simple semantics for the subjunctive conditional that is consistent with both CXM and Tooley’s counterexample.

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Minimalism deflated: independence without substance

The paper examines Wright’s attempt to inflate deflationism about truth. It accepts the details of Wright’s argument but contends that it should best be seen as posing a dilemma for the deflationist: either truth is independent of norms of warranted assertibility—in which case it is substantial—or it is not—in which case epistemicism about truth is a consequence. Some concerns about epistemicism are raised in avoiding the second horn. The first is avoided by distinguishing between independence and substantiality and arguing that only the first applies to truth and only the second is worrisome to deflationism. So, despite its sub-title, the following is not a diatribe against Home Rule but a modest defence of deflationism.     

Defending Conditional Excluded Middle

Lewis (1973) gave a short argument against conditional excluded middle, based on his treatment of ‘might’ counterfactuals. Bennett (2003) , with much of the recent literature, gives an alternative take on ‘might’ counterfactuals. But Bennett claims the might‐argument against CEM still goes through. This turns on a specific claim I call Bennett’s Hypothesis. I argue that independently of issues to do with the proper analysis of might‐counterfactuals, Bennett’s Hypothesis is inconsistent with CEM. But Bennett’s Hypothesis is independently objectionable, so we should resolve this tension by dropping the Hypothesis, not by dropping CEM.     

Conditional Excluded Middle in Systems of Consequential Implication

It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius' Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, which is intertranslatable with the modal logic KT, WBT is a theorem, so it is natural to ask which instances of CEM are derivable. We also investigate the systems CIw and CI of consequential implication, corresponding to the modal logics K and KD respectively, with occasional remarks about stronger systems. While unrestricted CEM produces modal collapse in all these systems, CEM restricted to contingent formulas yields the Alt2 axiom (semantically, each world can see at most two worlds), which corresponds to the symmetry of consequential implication. It is proved that in all the main systems considered, a given instance of CEM is derivable if and only if the result of replacing consequential implication by the material biconditional in one or other of its disjuncts is provable. Several related results are also proved. The methods of the paper are those of propositional modal logic as applied to a special sort of conditional.     

Semantic dispositionalism without exceptions

Philosophical Studies - Semantic Dispositionalism is roughly the view that meaning a certain thing by a word, or possessing a certain concept, consists in being disposed to do something, e.g.,...     

The Meaning of Being: Husserl on Existential Propositions as Predicative Propositions

Axiomathes - This essay examines how Husserl stretches the bounds of his philosophy of meaning, according to which all propositions are categorical, to account for existential propositions, which...     

论亚里士多德的排中律疑难

亚里士多德在《解释篇》第9章对排中律提出了限制. 亚里士多德说:"在有关现存事物或已发生的事物的场合,命题不论其为肯定的或否定的,都必须或为真的,或为假的.至于一对矛盾命题,则正如上面所已指出的,不论主词是普遍的并且命题是全称性的,或者主词是单称的,两个命题中其一必定为真的,而另一个必定为假的."[1]这里,亚里士多德就"有关现存事物或已发生的事物的场合"论述了排中律和矛盾律.     

Explicating Truth: Minimalism and Primitivism

This paper pursues two goals. The first is to show that Horwich's anti-primitivist version of minimalism must be rejected because, already for formal reasons, the truth-schema does not achieve a positive explication of any property of propositions. The second goal is to develop a more moderate primitivist version of minimalism according to which the truth-schema is admittedly powerless to underpin truth with something more basic but it still succeeds in giving a complete account of the necessary and sufficient conditions for a proposition to be true. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Semantic priming without awareness: Some methodological considerations and replications

Previous studies of subliminal semantic priming effects are considered. The distinction between subjective and objective detection thresholds proposed by Cheesman and Merikle (1984) is accepted, and it is concluded that no convincing evidence has been adduced to support or deny the existence of semantic priming effects at or below objective threshold. New criteria for the assessment of objective thresholds are proposed, and four experiments are reported in each of which pattern-masked primes were presented 10% below objective threshold. The first three experiments presented primes, mask, and targets binocularly; the fourth used dichoptic presentation. Data were analysed using both conventional F ratios and the quasi F ratio advocated by Clark (1973). Results showed that significant subliminal semantic priming effects occurred in each experiment when conventional F ratios were used, and significant effects occurred in all but the first experiment when quasi F was used. Binocular and dichoptic presentation of stimuli gave semantic priming effects whose magnitudes did not differ significantly. It is concluded that semantic priming effects can be obtained below objective detection threshold. It is also concluded that replication with different participants and different stimuli is preferable to the use of quasi F ratios in investigations where verbal stimuli are used.     

Semantic processing without conscious identification: evidence from event-related potentials

Three event-related potential (ERP) experiments examined whether semantic content can be accessed from visually presented words that cannot be consciously identified. Category labels were shown to participants, followed by masked, briefly exposed words that were either exemplars of the category or not exemplars. The task was to verify the category, by guessing if necessary, and to identify the word, naming it if possible. Exposure durations were selected to allow identification in approximately half the trials. For identified words, there was a marked difference in the ERP response between in-category and out-of-category words because of an N400 component. For unidentified words, there was a similar although smaller difference. Conscious identification was defined using a variety of approaches: verbal report, 6-alternative forced choice, and binary categorization (in the context of the regression method; A. G. Greenwald, M. R. Klinger, & E. S. Schuh, 1995). By any definition, ERPs for unidentified words showed evidence of semantic processing. In addition, there were differences in the neuronal populations recruited to process above-threshold versus below-threshold words, suggesting qualitative differences.     

Excluded from humanity: The dehumanizing effects of social ostracism

Humans have a fundamental need to form and maintain relationships. Social exclusion frustrates this need and has devastating psychological effects. The current research examines the relationship between social exclusion and the experience of dehumanization from the target’s perspective. When people were ostracized they judged themselves and those who ostracized them as less human (Studies 1 and 2), and believed they were viewed as less human by the perpetrators (Study 2). In both studies, essential ‘human nature’ was the dimension of humanness most sensitive to social exclusion.