Final answer:
The word that means "to defend an argument using established rules of logic" is 'justify'. This is crucial in fields that value structured argumentation, and differs from a theorem, conjecture, or assumption.
Step-by-step explanation:
The word defined as "to defend an argument using established rules of logic" is justify. When you justify an argument, you provide a rational basis for it, using logical reasoning and evidence. This concept of justification is important not only in mathematics but also in philosophy and other fields that rely on structured argumentation.
To further understand the context, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, like axioms. A conjecture is a proposition that is suspected to be true due to preliminary supporting evidence but has no proof. To assume is to take something as given without proof, often as a starting point for further reasoning.
In the process of scientific inquiry, a hypothesis is a proposed explanation for an event or a phenomenon. It is similar to a suggestion and it is tested to determine its validity. The scientific method often involves deductive reasoning, which entails starting with a general theory and applying it to specific instances to arrive at conclusions, and inductive reasoning, which involves making generalizations based on observations.