This essay on the social history of logic instruction considers the programmatic writings of Carnap/Neurath, but especially in the widely read book by Lillian Lieber, Mits, Wits and Logic, where Mits is the man in the street and Wits the woman in the street. In the ‘pre-Toulmin’ days it was seriously argued that the intense study of formal logic would create a more rational frame of mind and have many beneficial effects upon the social and political life. It arose from (...) the conviction that most metaphysical conundrums, religious and political problems and even fanaticism had their root in the irrationality of ordinary discourse, which had to be replaced by the more logical ‘ideal language’ of Principia Mathematica. The enthusiastic promotion of formal logic occurred at a time when it was widely thought that minds could be ‘made over’, ‘reprogrammed’ by proper intervention. This stands in stark contrast to the motivation for teaching informal logic and critical thinking, as it becomes apparent in a 1981 exchange between Ralph Johnson and Gerald Massey in Teaching Philosophy. Most of this essay focuses on Lillian Lieber, an earnest and enthusiastic advocate of the cause of formal logic, and on the reasons for the widespread conviction that, for the sake of peace and social harmony, formal logic should, if possible, be taught to every man, woman and child. (shrink)

We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and selection functions, independently of any strictness assumption.

A bivalent valuation is snt iff sound (standard PC inference rules take truths only into truths) and non-trivial (not all wffs are assigned the same truth value). Such a valuation is normal iff classically correct for each connective. Carnap knew that there were non-normal snt valuations of PC, and that the gap they revealed between syntax and semantics could be "jumped" as follows. Let $VAL_{snt}$ be the set of snt valuations, and $VAL_{nrm}$ be the set of normal ones. The bottom (...) row in the table for the wedge 'v' is not semantically determined by $VAL_{snt}$ , but if one deletes from $VAL_{snt}$ all those valuations that are not classically correct at the aforementioned row, one jumps straights to $VAL_{nrm}$ and thus to classical semantics. The conjecture we call semantic holism claims that the same thing happens for any semantic indeterminacy in any row in the table of any connective of PC, i.e., to remove it is to jump straight to classical semantics. We show (i) why semantic holism is plausible and (ii) why it is nevertheless false. And (iii) we pose a series of questions concerning the number of possible steps or jumps between the indeterminate semantics given by $VAL_{snt}$ and classical semantics given by $VAL_{nrm}$. (shrink)

This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction (...) between contradictories and contraries, and the square of opposition. This strategy helps to improve students’ understanding of metalogic, because it allows the students to integrate these new ideas with their previously acquired knowledge of syllogistics. (shrink)