Logic

1. Logic Chapter 3 Philosophy: Questions and theories

2. What is Logic? • Logical arguments consist of one or more claims or premises and a conclusion arranged in such a way that the premises are supposed to support the conclusion • E.g.: All smokers risk getting lung cancer. Alice is a smoker. Therefore, Alice risks getting lung cancer. • Premise 1 : All smokers risk getting lung cancer. • Premise 2: Alice is a smoker. • Conclusion: Alice risks getting lung cancer.

3. The Philosopher’s Approach to Logic • Logic involves two forms of reasoning: deduction and induction. • Deduction: goes from big picture to little picture/ general to specific • All cats are mammals • My pet is a cat • Therefore my pet is a mammal • For a good deductive argument you must have the premises as true and the argument must be valid • The premises must logically entail the conclusion

4. Induction: the process of observing particular things and making generalizations – drawing general conclusions • Swan 1 is white • Swan 2 is white • Swan 3 is white • Swan 1000 white • Therefore, all swans are white • Inductive arguments differ from deductive arguments in that their premises are supposed to support but not logically entail their conclusion • They are not deductively valid, the premises justify the conclusion

5. General Particular Deduction Induction

6. What Philosophers Have Said • Aristotle contributed to the logical thought with the three laws of thought • The law of non-contradiction say something cannot be said both to be and not to be at the same time and in the same respect • E.g.: If the statement, “Tom exists,” is true, it cannot also be false. • The law of the excluded middle says that something must either be or not be • E.g.: The statement, “Tom exists,” must either be true or not true. There is no middle. • The law of identity says that something is what it is • E.g.: To say that Tom is Tom and Sasha is Sasha is true while to say that Tom is Sasha is untrue.

7. Although modern logicians have developed systems that involve more than simply true or false possibilities, Aristotle’s laws still serve as primary tools for mathematics. • Francis Bacon (17th century) • Emphasized inductive reasoning as a tool of science and became the foundation of the scientific method. • 19th century George Boole • Developed Boolean/symbolic logic and used numbers and algebraic equations to represent chains of reasoning

8. How Philosophers Have Said It • An argument is a series of statements that consist of a premise or premises and a conclusion that follows from the premises. • A premise is a factual statement or proposition. • An argument is a response to a question and never opens with it or a command • Arguments start with statements that can be true or false. • Questions and commands are neither • Logical consistency means that the statements do not contradict each other to create a logical contradiction

9. A syllogism is a basic form of argument introduced by Aristotle and contains two premises and a conclusion • All humans are mortal (major premise) • I am human (minor premise) • Therefore I am mortal (conclusion) • “All” is a quantifier • Validity refers to the correctness of the reasoning and truth refers to the truth of the contents • All humans are immortal • Socrates is human • Therefore, he is immortal • Despite the truth of these statements, the argument is valid as the conclusion follows from the • Deductive reasoning is either valid or invalid but inductive arguments are reliable or weak • Logic is concerned with a form of argument and whether this form and the reasoning is correct