Logic: Apprehension, Judgement, and Reasoning

• The three main operations of the human mind are identified
• Different types of propositions and syllogisms are analyzed
• Logical reasoning is applied by constructing a valid syllogism

Simple Apprehension

• This is the mind's initial step in understanding
• It involves forming a basic idea of something without making any judgments about it
• A concept is the mental grasp of an obect or idea without affirming or denying anything about it
• A term is the verbal or written expression of a concept, for example, “TREE”
• Ideogenesis is the process by which the mind forms concepts through sensory perception and abstract understanding

Judgments and Propositions

• Judgment is when the mind affirms or denies something about a concept
• This leads to propositions
• Propositions are the building blocks of reasoning
• A proposition is a statement that combines two or more concepts and declares something true or false
• A proposition must have a subject and a predicate
• An example of an affirmative proposition is: “The sun is hot,” where "sun" is the subject and "hot" is the predicate
• An example of a negative proposition is: “Birds are not mammals,” where "birds" is the subject and "not mammals" is the predicate
• In the example of the negative proposition, the judgement denies that birds belong to the mammal category
• Logical relations between propositions are the connections that determine how propositions support or contradict each other
• These form the basis for logical reasoning
• Types of logical relations include contradiction, contrariety, and subalternation
• Contradiction means that one proposition must be true, and the other must be false
• “All dogs are friendly” and “Some dogs are not friendly” are an example of contradiction
• Contrariety means that both propositions can be false, but both can't be true at the same time
• "All politicians are honest” and “No politicians are honest” are an example of contrariety
• Subalternation means that if the general statement is true, the specific must be true too
• "All students must take exams” can lead to "Paul is a student, so he must take exams” as an example of subalternation

Reasoning

• Inference is the process of deriving a conclusion from one or more propositions
• “All men are mortal” and “Socrates is a man” can lead to an inference
• Syllogisms are structured arguments used in reasoning
• Categorical and Hypothetical are the two types of syllogisms
• Categorical syllogism is used when dealing with absolute statements like "all," "some," or "none."
• "All birds have feathers,” "An eagle is a bird,” and “Therefore, an eagle has feathers” is an example of a categorical syllogism
• Hypothetical Syllogism uses “if-then” logic
• “If it rains, the ground will be wet," “It is raining,” then "The ground is wet” is an example of a hypothetical syllogism