A 4-valued logic of strong conditional

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on affirmations and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3)

Exploring modality switching effects in negated sentences: further evidence for grounded representations

Theories of embodied cognition (e.g., Perceptual Symbol Systems Theory; Barsalou, 1999, 2009) suggest that modality specific simulations underlie the representation of concepts. Supporting evidence comes from modality switch costs: participants are slower to verify a property in one modality (e.g., auditory, BLENDER-loud) after verifying a property in a different modality (e.g., gustatory, CRANBERRIES-tart) compared to the same modality (e.g., LEAVES-rustling, Pecher et al., 2003). Similarly, modality switching costs lead to a modulation of the N400 effect in event-related potentials (ERPs; Collins et al., 2011; Hald et al., 2011). This effect of modality switching has also been shown to interact with the veracity of the sentence (Hald et al., 2011). The current ERP study further explores the role of modality match/mismatch on the processing of veracity as well as negation (sentences containing “not”). Our results indicate a modulation in the ERP based on modality and veracity, plus an interaction. The evidence supports the idea that modality specific simulations occur during language processing, and furthermore suggest that these simulations alter the processing of negation

The Laws of Thought

The Laws of Thought is an exploration of the deductive and inductive foundations of rational thought. The author here clarifies and defends Aristotle’s Three Laws of Thought, called the Laws of Identity, Non-contradiction and Exclusion of the Middle – and introduces two more, which are implicit in and crucial to them: the Fourth Law of Thought, called the Principle of Induction, and the Fifth Law of Thought, called the Principle of Deduction. This book is a thematic compilation drawn from past works by the author over a period of twenty-three years (1990-2013)

A Meta-Logic of Inference Rules: Syntax

This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the presence of the rule of reverse substitution, requires certain change the definition of structurality

Reality and the Meaning of Evil: On the Moral Causality of Signs

ABSTRACT: “Evil is really only a privation.” This philosophical commonplace reflects an ancient solution to the problem of theodicy in one of its dimensions: is evil of such a nature that it must have God as its author? Stated in this particular way, it also reflects the commonplace identification of the real with natural being—the realm of what exists independently of human thought and perspectives—as opposed to all that is termed, by comparison, “merely subjective” and “unreal”. If we stick with this way of construing the meaning of “reality”, then by the excellent arguments of the tradition we are also stuck with defending the sufficiency of privation as a response to what evil “really is”. In this article, we argue against both ways of being stuck. We argue, first, that a one-sided focus upon the being of nature blocks an adequate understanding of the world we actually live in: the semiotically constituted lifeworld that is the proper locus of human realities, including moral evil. We argue, second, that the positivity of moral evil consists not only, nor even primarily, in the positivity of “action” as such, but in structures of objectivity engendered by creative reason that oppose the due end, and that involve a specific genus of pure object which we call a mystical daydream. Like any objects, these objects are communicable and formative in relation to the lifeworld, within which they in turn engender further interpretants for both those who do and those who suffer evil, thanks to the causality of signs

Relevance and Conditionals: A Synopsis of Open Pragmatic and Semantic Issues

Recently several papers have reported relevance effects on the cognitive assessments of indicative conditionals, which pose an explanatory challenge to the Suppositional Theory of conditionals advanced by David Over, which is influential in the psychology of reasoning. Some of these results concern the “Equation” (P(if A, then C) = P(C|A)), others the de Finetti truth table, and yet others the uncertain and-to-inference task. The purpose of this chapter is to take a Birdseye view on the debate and investigate some of the open theoretical issues posed by the empirical results. Central among these is whether to count these effects as belonging to pragmatics or semantics

Raising argument strength using negative evidence: A constraint on models of induction

Both intuitively, and according to similarity-based theories of induction, relevant evidence raises argument strength when it is positive and lowers it when it is negative. In three experiments, we tested the hypothesis that argument strength can actually increase when negative evidence is introduced. Two kinds of argument were compared through forced choice or sequential evaluation: single positive arguments (e.g., “Shostakovich’s music causes alpha waves in the brain; therefore, Bach’s music causes alpha waves in the brain”) and double mixed arguments (e.g., “Shostakovich’s music causes alpha waves in the brain, X’s music DOES NOT; therefore, Bach’s music causes alpha waves in the brain”). Negative evidence in the second premise lowered credence when it applied to an item X from the same subcategory (e.g., Haydn) and raised it when it applied to a different subcategory (e.g., AC/DC). The results constitute a new constraint on models of induction

Differences in use and function of verbal irony between real and fictional discourse: (mis)interpretation and irony blindness

This paper presents a contrastive approach to the presence of two distinct types of verbal irony in real (natural, unscripted) versus fictional (scripted) discourse, with a special focus on irony blindness, i.e. the inability to recognize ironic utterances. Irony strategies are categorized into two general types, based on the relationship between the expressed and the intended meaning (Type 1: meaning reversal and Type 2: meaning replacement). First, the differences between these two types are discussed in terms of use, interpretation, and misinterpretation. It is found that the first type of irony strongly prevails in natural discourse, while the second type is considerably more present in fictional discourse than it is in natural discourse. At the same time, the first type of irony appears to be more at risk of misinterpretation in natural discourse, as opposed to the second type, which seems to be a safer (even though less frequently selected) option. These findings are then further analyzed in light of the discussion concerning fictional (comedic, in particular) irony blindness and the construction and role of the irony blind characters. Interestingly, the causes of fictional irony blindness are found to correlate more strongly with the (more humorous) misinterpretation of the second type of irony

Conceptual thinking in Hegel’s Science of logic

Filozofia analityczna po logicyzmie Fregego i atomizmie logicznym Russella odziedziczyła szereg założeń związanych z istnieniem rodzajowej dziedziny bytów indywidualnych, których tożsamość i elementarne określenia już mamy zdefiniowane. Te „indywidua” istnieją tylko w idealnych „światach możliwych” i nie są niczym innym jak zbiorami posiadającymi strukturę bądź czystymi zbiorami matematycznymi. W przeciwieństwie do takich czysto abstrakcyjnych modeli, Hegel analizuje rolę pojęciowych rozróżnień i odpowiednich brakujących inferencji w rzeczywistym świecie. Tutaj wszystkie obiekty są przestrzennie i czasowo skończone. Nawet jeśli rzeczywiste rzeczy poruszają się zgodnie z pewnymi formami, są tylko momentami w całościowym procesie. Wszelako, formy te nie są przedmiotami bezpośredniej, empirycznej obserwacji, lecz zakładają udane i powtarzalne działania i akty mowy. W rezultacie żadna semantyka odnoszącej się do świata referencji nie może obyć się bez kategorii Heglowskich, które wykraczają daleko poza narzędzia opartej wyłącznie na relacjach logiki matematycznej