Simplified semantics for relevant logics (and some of their rivals)

This paper continues the work of Priest and Sylvan inSimplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such asB ⁺ andB. We show that the simplified semantics can also be used for a large number of extensions of the positive base logicB ⁺, and then add the dualising^* operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.     

The Validity of a New,Self-report Measure of Multiple Intelligence

In all, 187 participants completed a new, self-report measure of eight multiple intelligences (Haselbauer 2005), a General Knowledge test (Irwing et al. Personality and Individual Differences 30:857–871, 2001), a measure of Approaches to Learning Styles (Biggs 1987), a measure of the Big Five personality traits (Costa and McCrae 1992), as well as gave their own estimated scores on the Gardner (1999) multiple intelligences. Alpha co-efficients were modest with only three of the eight test-derived, multiple intelligence scores being over .70. ‘Linguistic’ and Mathematical intelligence alone were correlated with General Knowledge. Five of the eight ‘intelligences’ were correlated both with Extraversion and Openness. Regressions indicated that ‘Intrapersonal intelligence’ was closely linked with Stability and Conscientiousness; ‘Interpersonal intelligence’ with Extraversion; ‘Linguistic intelligence’ with Openness; ‘Mathematical intelligence’ with Agreeableness and Conscientiousness. Correlations between self-estimated and test-derived emotional intelligence showed correlations ranging from r = .18 to r = .56 for similar type ‘intelligences’. This study provides modest evidence for the concurrent and construct validity of this measure. It requires more psychometric evidence of validity before it is used.     

A Defense of the Principle of Indifference

The principle of indifference (hereafter ‘Poi’) says that if one has no more reason to believe A than B (and vice versa), then one ought not to believe A more than B (nor vice versa). Many think it’s demonstrably false despite its intuitive plausibility, because of a particular style of thought experiment that generates counterexamples. Roger White (2008) defends Poi by arguing that its antecedent is false in these thought experiments. Like White I believe Poi, but I find his defense unsatisfactory for two reasons: it appeals to false premises, and it saves Poi only at the expense of something that Poi’s believers likely find just as important. So in this essay I defend Poi by arguing that its antecedent does hold in the relevant thought experiments, and that the further propositions needed to reject Poi are false. I play only defense in this essay; I don’t argue that Poi is true (even though I think it is), but rather that one popular refutation is faulty. In showing this, I also note something that has to my knowledge gone unnoticed: given some innocuous-looking assumptions the denial of Poi is equivalent to a version of epistemic permissivism, and Poi itself is equivalent to a version of epistemic uniqueness.     

A Routley-Meyer affixing style semantics for logics containing Aristotle's Thesis

We provide a semantics for relevant logics with addition of Aristotle's Thesis, ∼(A→∼A) and also Boethius,(A→B)→∼(A→∼B). We adopt the Routley-Meyer affixing style of semantics but include in the model structures a regulatory structure for all interpretations of formulae, with a view to obtaining a lessad hoc semantics than those previously given for such logics. Soundness and completeness are proved, and in the completeness proof, a new corollary to the Priming Lemma is introduced (c.f.Relevant Logics and their Rivals I, Ridgeview, 1982).     

Local contexts and local meanings

Stalnaker (1978) made two seminal claims about presuppositions. The most influential one was that presupposition projection is computed by a pragmatic mechanism based on a notion of ‘local context’. Due to conceptual and technical difficulties, however, the latter notion was reinterpreted in purely semantic terms within ‘dynamic semantics’ (Heim 1983). The second claim was that some instances of presupposition generation should also be explained in pragmatic terms. But despite various attempts, the definition of a precise ‘triggering algorithm’ has remained somewhat elusive. We discuss possible extensions of both claims. First, we offer a reconstruction of ‘local contexts’ which circumvents some of the difficulties faced by Stalnaker’s original analysis. We preserve the idea that local contexts are computed by a pragmatic mechanism that aggregates the information that follows from an incomplete sentence given the global context; but we crucially rely on a modified notion of entailment (‘R-entailment’), whose plausibility should be assessed on independent grounds. Second, we speculate that local contexts might prove necessary (though by no means sufficient) to understand how some presuppositions are triggered. In a nutshell, we suggest that a presupposition is triggered when the semantic contribution of an expression to its local context is in some sense ‘heterogeneous’. Without giving an analysis of the latter notion, we note that this architecture implies that presuppositions should be triggered on the basis of the meaning that an expression has relative to its local context (what we call its ‘local meaning’); we sketch some possible consequences of this analysis.     

Yet Another Run around the Circle

In a recent article, D. A. Truncellito (2004, ‘Running in Circles about Begging the Question’, Argumentation 18, 325–329) argues that the discussion between Robinson (1971, ‘Begging the Question’, Analysis 31, 113–117), Sorensen (1996, ‘Unbeggable Questions’, Analysis 56, 51–55) and Teng (1997, ‘Sorensen on Begging the Question’, Analysis 57, 220–222) shows that we need to distinguish between logical fallacies, which are mistakes in the form of the argument, and rhetorical fallacies, which are mistakes committed by the arguer. While I basically agree with Truncellito’s line of thinking, I believe this distinction is not tenable and offer a different view. In addition, I will argue that the conclusion to draw from the abovementioned discussion is that validity is not a sufficient criterion of begging the question, and that we should be wary of the containment-metaphor of a deductive argument.     

Attesting the Aristotelian Future

Aristotelian relativism about the future (as recently defended by MacFarlane (2003)) claims that a prediction made on Monday, such as ‘It will rain’, can be indeterminate on Monday but determinate on Tuesday. A serious objection to this intuitively appealing view is that it cannot coherently be attested: for if it is attested on Monday, then our blindness to what the future holds precludes attesting that the prediction is determinate on Tuesday, and if it is attested on Tuesday (when, suppose, it rains), then the fact that it rains precludes attesting that the prediction is indeterminate on Monday. In this paper, I focus on Moruzzi and Wright (2009)’s recent development of this objection and argue that it fails. This result removes a major obstacle to defending the Aristotelian view.     

Emotion and ethics: An inter-(en)active approach

In this paper, we start exploring the affective and ethical dimension of what De Jaegher and Di Paolo (Phenomenology and the Cognitive Sciences, 6:485–507, 2007) have called ‘participatory sense-making’. In the first part, we distinguish various ways in which we are, and feel, affectively inter-connected in interpersonal encounters. In the second part, we discuss the ethical character of this affective inter-connectedness, as well as the implications that taking an ‘inter-(en)active approach’ has for ethical theory itself.     

The Genesis of Hi-Worlds: Towards a Principle-Based Possible World Semantics

A Leibnizian semantics proposed by Becker in 1952 for the modal operators has recently been reviewed in Copeland’s paper The Genesis of Possible World Semantics (Copeland in J Philos Logic 31:99–137, 2002), with a remark that “neither the binary relation nor the idea of proving completeness was present in Becker’s work”. In light of Frege’s celebrated Sense-Determines-Reference principle, we find, however, that it is Becker’s semantics, rather than Kripke’s semantics, that has captured the true spirit of Frege’s semantic program. Furthermore, for Kripke’s possible world semantics to fit in Frege’s framework of senses, worlds and referents, it will have to be thoroughly reformulated. By introducing the notion of a hi-world into the picture, we manage to keep the key ingredients of Becker’s semantics intact, while at the same time solve a fatal problem that used to shadow Becker’s original semantics—it had not been able to make sense of inhomogeneous modality. The resulting generalized Beckerian semantics provides, in effect, a Beckerian analysis of the Kripkean possible worlds. It reveals the subtle hierarchical internal structure of a Kripkean world that has not been discovered before.     

Sensing Aliveness

This study examines whether the categories animate/inanimate might be formed on the basis of information available to the cognitive system. We suggest that the discrimination of percepts according to these categories relies on proprioceptive information, which allows the perceiving subject to know that he is ‘animate’. Since other ‘objects’ in the world exhibit movements, reactions, etc. similar to those that the subject experiences himself, he can ‘project’ his knowledge onto these objects and recognize them as ‘animate’ like himself. On this basis we try to corroborate the empricist position in the debate concerning the organization of knowledge as opposed to the nativist view. Furthermore, we argue that the categorical dichotomy animate/inanimate is more basic than other analogous ones such as living/non-living, biological/non-biological and we sketch a ‘categorical stratification’ following the line ‘humans–animals–plants’ based on the hypothesis that humans detect different degrees of ‘vitality’ according to the degree of similarity they recognise between the considered instance and themselves.     

A positional coding mechanism in pigeons after learning multiple three-item lists

Pigeons were trained on three three-item lists (List 1: A₁ → B₁ → C_1; List 2: A₂ → B₂ → C_2; List 3: A₃ → B₃ → C₃). After sessions in which any one of the three lists could be presented on a trial, derived-maintained list and derived-changed list probe trials were introduced. The derived list probe trials were composed of three items, one drawn from each of the training lists. On derived-maintained probe trials, each item was in the same ordinal position it occupied during training (e.g., A₃ → B₁ → C₂). On derived-changed probe trials, items that occupied the second and third position during training were exchanged (e.g., A₂ → C₃ → B₁). The performance of subjects on derived-maintained probe trials was significantly above chance and no different to that observed on the training lists. In contrast, subjects’ performance on derived-changed probe trials was significantly below chance. To our knowledge, this is the first study that has demonstrated pigeons are able to learn and retain multiple three-item lists. In addition, subjects’ performance on the derived-maintained probe trials suggests that they acquire knowledge of each list item’s ordinal position when learning multiple lists.     

Time for Presence?

It is, I think, possible to generate a variation of McTaggart’s (Mind 17:457–474, 1908) paradox that infects all extant versions of presentism. This is not to say that presentism is doomed to failure. There may be ways to modify presentism and I can’t anticipate all such modifications, here. For the purposes of the paper I’ll understand ‘presentism’ to be the view that for all x, x is present (cf. Crisp (2004: 18)). It seems only right that, at a conference devoted to McTaggart’s work on time, we continue to pursue new ways in which his now infamous arguments remain relevant to us today.     

Shifting Loyalties: Reconsidering Psychology’s Subject Matter

Schwarz (IPBS: Integrative Psychology & Behavioral Science 43:3, 2009) cogently demonstrates that in conjunction with scientific conventionalism psychology has developed a rather deficient view of their subject matter: the human being. Psychology based on an impoverished notion of empirical has rendered subjectivity or ‘the measuring apparatus man’ invisible. As his story implicitly demonstrates, psychologists supported by a positivistic view of science (in part to be empirical) and notion of ‘objectivity’ have learned to trust their ‘rigorous’ methods instead of their participants as capable of revealing important and interesting phenomena. If we are going to take subjectivity and experience seriously there should be a cultivation of a new attitude or orientation regarding psychology’s subject matter (i.e., the human being) and science. This commentary discusses Mark Freeman’s (2007) argument that the first requirement of science should be ‘fidelity to the phenomena’ and elaborates on the implications for psychology grounded in this view of science.     

Thomason’s Paradox for Belief,and Two Consequence Relations

Thomason (1979/2010)’s argument against competence psychologism in semantics envisages a representation of a subject’s competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject’s beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain ‘natural assumptions’, then it implies that the subject is inconsistent if the beliefs include arithmetic. I challenge the result by insisting that the motivation for Thomason’s principle (ii), via Moore’s Paradox, leads to a more complex representation, in which stating the facts and expressing one’s beliefs are treated differently. Certain logical connections among expressions of assent, and between expression and statement, are a matter of consequence on pain of pragmatic incoherence, not consequence on pain of classical logical inconsistency. But while this salvages the possibility that a modification of the above sort of representation could be adequate, Thomason’s devastating conclusion returns if the scientist identifies himself as the subject of that representation, even when paying heed to the requirement of pragmatic coherence of the sort highlighted by Moore’s Paradox.     

The Logic of Theory Assessment

This paper starts by indicating the analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper consists in working out the claim that one can have Hempel’s cake and eat it too — in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, α is an acceptable theory for evidence β if and only if α is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap’s positive relevance account, thereby shedding new light on Carnap’s analysis as well as solving another problem of confirmation theory. A precursor of this paper has appeared as “The Logic of Confirmation and Theory Assessment” in L. Běhounek & M. Bílková (eds.), The Logica Yearbook 2004, Prague: Filosofia, 2005, 161–176.     

Vollkommene Syllogismen und reine Vernunftschlüsse: Aristoteles und Kant. Eine Stellungnahme zu Theodor Eberts Gegeneinwänden. Teil 2

In an earlier article (see J Gen Philos Sci (2010) 41: 341–355) I have compared Aristotle’s syllogistic with Kant’s theory of “pure ratiocination”. “Ratiocinia pura” („reine Vernunftschlüsse“) is Kant’s designation for assertoric syllogisms Aristotle has called ‘perfect’. In Kant’s view they differ from non-pure ratiocinia precisely in that their validity rests only on the validity of the Dictum de omni et nullo (which, however, in Kant’s view can be further reduced to more fundamental principles) whereas the validity of non-pure ratiocinia additionally presupposes the validity of inferences which Kant calls consequentiae immediatae. I have argued that Kant’s view is in some (not in all) essential features in accordance with Aristotle’s view concerning perfect syllogisms and certainly leading to a tenable and interesting logical theory. As a result I have rejected not only the interpretation of Aristotle adopted by Theodor Ebert, but also the objections he has raised against Kant’s logical theory. As far as Aristotle is concerned, Ebert has attempted to defend his position in the first part of his reply to my article published in J Gen Philos Sci (2009) 40: 357–365, and I have argued against this defence in issue 1 of the J Gen Philos Sci (2010) 41: 199–213 (cf. Ebert’s answer in the same issue pp. 215–231). In the following discussion I deal with Eberts defence of his criticism of Kant published in the second part of his reply to my article (see J Gen Philos Sci (2009) 40: 365–372). I shall argue, that Kant’s principle ‘nota notae est nota rei ipsius’ and his use of technical vocabulary stand up to the objections raised by Ebert. His attempts to prove that Kant’s logical theory is defective are based on several misinterpretations.     

What <Emphasis Type="Italic">ought</Emphasis> probably means,and why you can’t detach it

Some intuitive normative principles raise vexing ‘detaching problems’ by their failure to license modus ponens. I examine three such principles (a self-reliance principle and two different instrumental principles) and recent stategies employed to resolve their detaching problems. I show that solving these problems necessitates postulating an indefinitely large number of senses for ‘ought’. The semantics for ‘ought’ that is standard in linguistics offers a unifying strategy for solving these problems, but I argue that an alternative approach combining an end-relational theory of normativity with a comparative probabilistic semantics for ‘ought’ provides a more satisfactory solution.     

Why the Hardest Logic Puzzle Ever Cannot Be Solved in Less than Three Questions

Rabern and Rabern (Analysis 68:105–112 2) and Uzquiano (Analysis 70:39–44 4) have each presented increasingly harder versions of ‘the hardest logic puzzle ever’ (Boolos The Harvard Review of Philosophy 6:62–65 1), and each has provided a two-question solution to his predecessor’s puzzle. But Uzquiano’s puzzle is different from the original and different from Rabern and Rabern’s in at least one important respect: it cannot be solved in less than three questions. In this paper we solve Uzquiano’s puzzle in three questions and show why there is no solution in two. Finally, to cement a tradition, we introduce a puzzle of our own.