Kamp and Fine presented an influential argument against the use of fuzzy logic for linguistic semantics in 1975. However, the argument assumes that contradictions of the form "A and not A" have semantic value zero. The argument has been recently criticized because sentences of this form are actually not perceived as contradictory by naive speakers. I present new experimental evidence arguing that fuzzy logic still isn't useful for linguistic semantics even if we take such naive speaker judgements at face value. (...) Specifically I show that naive speakers judge "A and not A" in the relevant cases as more true than "B and not A" even when A and B are judged to be equally true. A truth functional semantics such as fuzzy logic cannot account for these intuitions directly. (shrink)

We here propose a solution to the problem we have raised. Basically, the mathematical notion of entailment seems to be connected to the inferential rules from Classical Logic, so that if we have P: x belongs to the reals, and Q: x+2=5 => x=3, P |= Q. Notwithstanding, we would also have that if P: x belongs to the interval (7,10), and Q: x+2=5 => x=3, P |= Q. The second instance of entailment does not seem to be justifiable if (...) our intuition is consulted: Even though we could say that absurdity implies anything in Classical Logic, entailment should be a concept that belongs to the metalogic, not to the logic of the system, so that we should not be inside of the Classical Logic World by the time we assess things in what regards entailment. As another point, our discussions in Entailment led us to choose the sense has as a consequence for entailment, so that it is not really acceptable that we have, as a consequence, using normal language, of x being inside of the real interval (7,10) that if x+2=5, then x=3. If x is in that interval, x+2 should not be 5, unless we are talking about moduli of vectors. However, when we transfer to Classical Logic, in having the antecedent false, and the consequent false as well, we have that the implication, which some call material, is true. We here discuss this sort of matter in detail, and hope to get to the bottom of the issue, and perhaps to a universal solution. (shrink)

This paper argues that general skills and the varieties of subject-specific discourse are both important for teaching, learning and practising critical thinking. The former is important because it outlines the principles of good reasoning simpliciter (what constitutes sound reasoning patterns, invalid inferences, and so on). The latter is important because it outlines how the general principles are used and deployed in the service of ‘academic tribes’. Because critical thinking skills are—in part, at least—general skills, they can be applied to all (...) disciplines and subject-matter indiscriminately. General skills can help us assess reasoning independently of the vagaries of the linguistic discourse we express arguments in. The paper looks at the debate between the ‘specifists’—those who stress the importance of critical thinking understood as a subject-specific discourse—and the ‘generalists’—those that stress the importance of critical thinking understood independently of disciplinary context. The paper suggests that the ‘debate’ between the specifists and the generalists amounts to a fallacy of the false alternative, and presents a combinatory-‘infusion’ approach to critical thinking. (shrink)

Entailment is an interesting sigmatoid: It should mean one thing, but it means another, just for starters. When used in Mathematics, it is usually with the sense of saying that something is definitely true. That would be the use in Classical Logic then. When used in Logic, it became something else. Now it was about how the logical system, which can be any nonclassical one, could be making a proposition become true or false. The major issue we found in 2000, (...) when learning from the own nonclassicists what they do, was that they talk about Nonclassical Logic, therefore a way of thinking that is not Cartesian, yet they stick to the notion of entailment we use in Mathematics, and therefore to the Classical Logic ways. We here discuss exactly this. (shrink)

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.

Naive speakers find some logical contradictions acceptable, specifically borderline contradictions involving vague predicates such as Joe is and isn’t tall. In a recent paper, Cobreros et al. (J Philos Logic, 2012) suggest a pragmatic account of the acceptability of borderline contradictions. We show, however, that the pragmatic account predicts the wrong truth conditions for some examples with disjunction. As a remedy, we propose a semantic analysis instead. The analysis is close to a variant of fuzzy logic, but conjunction and disjunction (...) are interpreted as intensional operators. (shrink)