COT 3100C - 2/17

Begin with accepting certain propositions as true to establish a basis for inference. This helps in constructing logical frameworks.
Example: Accepting that if taxes are lowered, changes in automatic inferences will follow. In this scenario, one could infer potential outcomes such as increased consumer spending or investment based on historical economic trends.

From accepted premises, derive conclusions logically, ensuring that these conclusions align without contradictions or fallacies in reasoning. Each step of inference must maintain validity.
It is important to ensure that all propositions are accounted for in the reasoning process, which prevents overlooked nuances from distorting the conclusions.

Testing Validity: To check if an argument is valid, attempt to demonstrate its validity through specific values and outcomes. For instance, Example: Assuming the square root of 2 is greater than 3/2 as a true premise. One would explore whether this argument holds by substituting values in various mathematical models or theorizing about additional number properties.
Using Contrapositives: A method to simplify proving the validity of an argument. Revisiting statements and their contrapositives can help ascertain the soundness of the argument more easily. For instance, demonstrating the relationship between a statement and its contrapositive can often reveal truthfulness in less direct ways.

Quantifiers and Rules of Inference: Understanding how to use quantifiers and different rules of inference effectively is fundamental in logic. This includes how to apply universal and existential quantifiers in statements to critically assess the generalizations made.
Utilize extension and instantiation in logical proofs after introducing quantifiers: This foundational knowledge is necessary for advancing into more complex logical reasoning. Mastery of these concepts allows for the construction of persuasive arguments and accurate problem-solving in various disciplines, from mathematics to social sciences.