1. Objectives
Define logic, identify argument components, understand sentences and passages.
2. Timeline of Logicians 🌴
Aristotle 🌴 The Megarians 🌴 Stoics 🌴 Boethius 🌴 Avicenna 🌴 Leibniz 🌴 Peirce 🌴 Wittgenstein 🌴
3. What is Logic? What is an Argument?
Logic studies correct reasoning and develops methods for evaluating expressions of reasoning. It is the organized body of knowledge that evaluates arguments.
An argument is a group of statements, one or more of which (the premises) are claimed to provide support for or reasons to believe one of the others (the conclusion).
The connection between the premises and the conclusion is called the inferential link:
- Premise One: All horses are mammals.
- Premise Two: No mammals are reptiles.
- Conclusion: No horses are reptiles.
- Premise 1: If the bridge is closed, then no one can get to the island.
- Premise 2: The bridge is closed.
- Conclusion: No one can get to the island.
4. Bivalent vs Non-Bivalent Sentences
Thoughts can be expressed in language. Example: “Sheep jump over fences.” The subject phrase is “sheep.” The predicate phrase is “jumps over fences.”
Active Learning Prompt:
State the subject phrase of the sentence: "Female crabs that live in the James River are rare."
Formal vs Informal Languages
Informal languages (e.g., English, Japanese) arise naturally. Formal languages (e.g., Javascript, formal logic) are invented for specific purposes.
Examples of Bivalent Sentences
- New York City is a city in the United States.
- Chert is not a type of quartz.
- Full-time students should spend 36–42 hours per week on schoolwork.
Examples of Non-Bivalent Sentences
- Questions: How far is Cleveland from Naples?
- Commands: Stand up.
- Exclamations: Whew!
- Humor: "A burrito is a sleeping bag for ground beef."
- Suggestions: Maybe use route 5 next time instead of I-64.
- Expressions of Wishes: Wish you the best!
- Nonsense: 'Twas brillig, and the slithy toves did gyre and gimble in the wabe.
Reflection Activity:
Analyze why the sentence "Colorless green ideas sleep furiously" fails to express a coherent thought.
5. How to Assess Reasoning
Steps:
- Look for reasoning indicator words.
- Conclusion indicators include: therefore, hence, thus, ergo, so, it follows that, consequently, this entails that, and similar terms.
- Premise indicators include: since, because, for the reason that, it follows from, assuming that, etc.
Active Learning Prompt:
Match each indicator to whether it suggests a premise or a conclusion:
- Since
- Consequently
- Hence
- Given that
- Therefore
- Because
6. Non-Inferential Passage Types
Types:
- Report: Conveys information about an event.
- Statement of Belief: Expresses a group or individual's belief.
- Explanation: Answers "why" something happens.
- Illustration: Demonstrates or exemplifies a concept.
- Advice/Warning: Recommends action or alerts about danger.
Active Learning Prompt:
Identify which type each passage belongs to:
- Studies have shown that some groups of people may be affected more by post-COVID conditions. These are examples: People who have experienced more severe COVID-19 illness; People who had underlying health conditions prior to COVID-19; People who did not get a COVID-19 vaccine.
- Ask yourself: More importantly, do you know your friend well enough to judge whether she would be grateful or embarrassed?
- People wonder why toothpaste and O.J. taste awful together. Toothpaste contains sodium lauryl sulfate (SLS) that creates bubbles when you brush. But it suppresses sweet receptors on the tongue, which prevents the brain from registering sweetness, and destroys compounds in the saliva called phospholipids, which block bitter receptors. SLS not only cuts orange juice’s sweetness, but promotes its natural bitterness, too. So, that is why.
- One of the most costly chemical disasters in the United States involved a small, single-product manufacturer, ironically named Life Science Products Company, which made the pesticide Kepone…[it] operated only 16 months in 1974 and 1975, in Hopewell, Virginia, yet managed to poison its workers and pollute the environment, causing millions of dollars of damage.
- But we refuse to believe that the bank of justice is bankrupt. We refuse to believe that there are insufficient funds in the great vaults of opportunity of this nation.
