The Comparative Set Fallacy

This paper argues for the validity of inferences that take the form of: A is more X than B; therefore A and B are both X. After considering representative counterexamples, it is claimed that these inferences are valid if and only if the comparative terms in the inference are taken from no more than one comparative set, where a comparative set is understood to be comprised of a positive, comparative, and superlative, represented as {X, more X than, most X}. In all instances where arguments appearing to be of this form are invalid, it is the case that the argument has fallaciously taken terms from more than one comparative set. The fallacy of appealing to more than one comparative set in an inference involving comparative terms is shown to be analogous to the fallacy of equivocation in argumentation. The paper concludes by suggesting a conflation of logical issues with grammatical issues is the core difficulty leading some to consider inferences in the form of A is more X than B; therefore A and B are X to be invalid.     

Penrose's New Argument

It has been argued, by Penrose and others, that Gödel's proof of his first incompleteness theorem shows that human mathematics cannot be captured by a formal system F: the Gödel sentence G(F) of F can be proved by a (human) mathematician but is not provable in F. To this argment it has been objected that the mathematician can prove G(F) only if (s)he can prove that F is consistent, which is unlikely if F is complicated. Penrose has invented a new argument intended to avoid this objection. In the paper I try to show that Penrose's new argument is inconclusive.     

Children's comprehension of visual formal features in television programs

A review of previous studies on children's comprehension of visual formal features did not warrant predictions about children's understanding of the formal features as used in three items from Sesamstraat, the Dutch version of Sesame Street. Therefore, a study was designed in which 45 children in the age range of 4–6 years watched the items and were interviewed. In the first item, a split screen was used to visualize simultaneity of actions. The second item used a subjective camera to suggest the construction of a home video by one of the characters. Version 1 of this item did not show the character while making home video, whereas Version 2 did show the character while filming. The third item contained a dissolve (Version 1) or a cut (Version 2) to indicate the end of a dream. A general conclusion was that although older children (mean AGE=5.9 years) understood the visual formal features better than younger children (mean AGE=4.4 years), the extent to which children in both age groups understood the visual formal features appeared to vary between items and versions. Most children in both age groups understood the split screen in the first item. The younger age group did not understand the subjective camera if the making of the home video was not shown. Both the younger and the older age group understood the version with the cut better than the original version with the dissolve. In the discussion, the question was addressed what the findings of this study and previous studies teach us about children's understanding of visual formal features in general.     

The Straw Thing of Fallacy Theory: The Standard Definition of 'Fallacy'

Hamblin held that the conception of 'fallacy' as an argument that seems valid but is not really so was the dominant conception of fallacy in the history of fallacy studies. The present paper explores the extent of support that there is for this view. After presenting a brief analysis of 'the standard definition of fallacy,' a number of the definitions of 'fallacy' in texts from the middle of this century – from the standard treatment – are considered. This is followed by a review of the definitions of 'fallacy' in the earlier history of logic books, including those of Aristotle, Whately, Mill and De Morgan. The essay concludes that there is scarcely any support for Hamblin's view that this particular definition of 'fallacy' was widely held.