Abstract
This paper is a study of various strategies for teaching syllogistics as part of a course in basic logic. It is a continuation of earlier studies involving practical experiments with students of Communication using the Syllog system, which makes it possible to develop e-learning tools and to do learning analytics based on log-data. The aim of the present paper is to investigate whether the Syllog e-learning tools can be helpful in logic teaching in order to obtain a better understanding of logic and argumentation in general and syllogisms in particular. Four versions of a course in basic logic involving different teaching methods will be compared.
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Notes
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- 2.
We may express these functors in terms of first order predicate calculus in the following way:
The four basic propositions can be related in terms of negation:
The classical syllogisms occur in four different figures:
where u, v, w \(\in \) {a, e, i, o} and where M, S, P are variables corresponding to “the middle term”, “the subject” and “the predicate” (of the conclusion).
- 3.
It should be noted that (TRANS), which is in fact short for ‘transitivity’, may in fact be read as the syllogism barbara in Fig. 1. Furthermore, by substituting Z by non-Z we get the syllogism celarent in Fig. 1. — Similarly, it is obvious that (SUBST), which is short for ‘substitution’, leads directly to the syllogism darii in Fig. 1, and if Z is replaced by non-Z we get ferio in Fig. 1. The three remaining rules are different from the first two in the sense that they only depend on one premise each. (CONTRA) — which is short for ‘contraposition’ — makes it possible to transform a universally quantified proposition, whereas (MUT) — which is short for ‘mutation’ — makes it possible to transform an existentially quantified proposition. (EX) — which is short for ‘existence’ — makes it possible to derive an existentially quantified proposition from a universally quantified proposition.
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Using this deductive approach to the syllogisms, it is possible to show a number of interesting results concerning the invalidity of certain syllogistic arguments. For instance, by going through the five rules of inference it is evident that if both premises are existential, then nothing new follows regarding the relation between subject and predicate. The same holds if both premises are negative i.e. o-propositions or e-propositions. The use of the inference rule (EX) has sometimes been seen as controversial, and the 9 syllogisms which depend on this rule have consequently been seen as “questioned”. Clearly (EX) has to be rejected, if we hold that the statement “all S are P” is true given that S is the empty set. Therefore, if this is accepted it should obviously not be permitted to deduce “some” from “all”. If the EX rule is excluded, the number of valid syllogisms is reduced from 24 to 15.
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Øhrstrøm, P., Sandborg-Petersen, U., Thorvaldsen, S., Ploug, T. (2017). Teaching Syllogistics Using E-learning Tools. In: Vincenti, G., Bucciero, A., Helfert, M., Glowatz, M. (eds) E-Learning, E-Education, and Online Training. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-319-49625-2_13
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