Conditional statements in mathematics and beyond: Syntax, semantics, and context

Thesis type
(Thesis) Ph.D.
Date created
Logic is an inseparable part of mathematics and is ubiquitous everywhere, such as in definitions, in theorem statements, in proofs, etc. This thesis starts with a discussion about the significant role of logic, both in formal mathematics and in informal mathematics, that includes all mathematical discussions in everyday language, with the main focus on conditional statements. A conditional statement does not have a fixed definition and has different interpretations in colloquial language, philosophy, logic, and mathematics. Mathematics uses the same definition as the one defined in logic, known as a material conditional. However, this definition is different from the interpretations in other disciplines, which makes it a topic that causes difficulties for students, especially when conditionals have irrelevant antecedents and consequents. This thesis discusses word problems in mathematics and explains why mathematics needs to include conditionals with irrelevant clauses. Like any other language, logic has its own semantics and syntax, but, besides the logical form of a statement, its context can influence the way people understand them. The current work adds a third component, namely context, to syntax and semantics of logic as a language, and details two studies to show that the context of a conditional statement is a determinative factor in understanding them. The first study examines how a mathematician with a good background in elementary logic understands conditional statements in different contexts of logic, mathematics, and colloquial language. The data are created through a clinical interview designed in three formats: structured, semi-structured, and non-structured. I also extend Stephen Toulmin's argumentation scheme to capture more features of the events and prepare data for analysis. The second study examines the language that thirty-four prospective elementary school teachers use and understand when dealing with situations involving conditional sentences; data is collected through a questionnaire. The theory of mental models is used to analyze data for both studies. The results from the research studies of this thesis show that the context can highly influence people's understanding of a conditional statement, and they mostly choose the type of conditionals present in everyday language.
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Supervisor or Senior Supervisor
Thesis advisor: Zazkis, Rina
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