Reasoning about Reasoning

1. Reasoning about Reasoning Philosophy: Thinkers, Theories, and Questions Chapter 1

2. What is Reasoning? • Reasoning is an all-pervasive activity in which one engages when reassessing ideas, assessing the merits of other ideas and assessing claims made in the media • Reasoning is thinking in accordance with standards o reasoning and being on guard against prejudices in our thinking • Related to autonomy; the ability to be master of our thoughts and behaviours when making up own minds

3. Why is good reasoning important? • It helps us make decisions • Helps us avoid manipulation • Helps us determine the validity of information and use this information effectively • Helps us defend our positions • Helps us make sense of our world

4. General Principles of Reasoning • Aristotle was one of the first philosophers to undertake a systematic and comprehensive examination of the reasoning process • In Organon he identified some general principles of reasoning and found the branch of reasoning we now call formal logic • Formal logic is dedicated to the study of deductive arguments

5. General Principles of Reasoning (cont) • Three laws of thought are law of identity, the law of non-contradiction and law of excluded middle • Fundamental in the sense that with out them our reasoning is incoherent, confused and faulty

6. Propositions • A proposition is a statement that is considered to be either true or false • E.g.: Your room is messy • The shape of the Earth is close to the shape of a sphere • The moon is made of cheese • Capital punishment is never justified. • The truth or falsity of some propositions may be a matter of much debate, some are true only a certain times, and some are always true

7. The Law of Identity • The law of identity states that A is A • The identity of a thing has to do with the actual properties that a thing possesses and without which it would not be the thing in question

8. The Law of Non-contradiction • The law of non-contradiction states that a proposition cannot be true and false at the same time in the same respect • A contradiction occurs when a proposition is held to be both true and false at the same time and in the same respect

9. The Law of Excluded Middle • The law of the excluded middle states that a specific proposition is either true or false • There is no middle ground • The truth of the proposition may depend on the meaning of the terms used • The law of excluded middle enable us to assign a truth-value to a proposition • Declares whether a proposition is true or false

10. The Principle of Sufficient Reason • The principle of sufficient reason states that everything must have a reason or cause • Attributed to Gottfried Leibniz • Three versions: • For every entity X, if X exists, then there is a sufficient explanation for why X exists • For every event E, if E occurs, then there is a sufficient explanation for why E occurs • For every proposition P, if P is true, then there is a sufficient explanation for why P is true

11. Ockham ’s Razor • Ockham’s razor is named after Franciscan friar and logician, William Ockham • Ockham stated that we should avoid multiplying entities beyond necessity to help us figure out which theory or explanation seems most true in a given situation • E.g.: You tell your teacher that aliens took your textbook. • Using Ockham’s razor your teacher would choose not to believe you because the loss of the textbook could be explained without aliens

12. Ockham’s Razor (cont) • When trying to figure out which theory or explanation is true in a given situation, the simplest theory is the best choice • It makes the fewest assumptions and entities to explain the same facts • If the simplest theory cannot explain the facts then a more complicated one should be used

13. Reasoning and Arguments • An argument consists of propositions that the arguer takes as true with one particular proposition, the conclusion, argued for by using the other propositions, the premises

14. Reasoning and Arguments (cont) • Consider this: • “Capital punishment should not be used because wrongly convicted people will be executed by mistake and this is totally unacceptable.” • P1: If capital punishment is used, then wrongly convicted people will be executed by mistake. • P2: The execution of wrongly convicted people is totally unacceptable. • C: Capital punishment should not be used. • P1 refers to the first premise, P2 refers to the second premise and C refers to the conclusion

15. Conclusion-Indicators and Premise-Indicators • Certain words are commonly used to introduce premises and conclusions • However, not every argument contains indicators: • E.g.: “There is no such thing as free will. The mind is induced to wish this or that by some cause, and that cause is determined by another cause, and so on back to infinity.” Baruch Spinoza

16. Conclusion-Indicators and Premise-Indicators (cont) • Also the presence of an indicator is no guarantee that there is an argument • E.g.: “Dinosaurs are extinct because of the impact of a large asteroid,” and “I have to get up early so I will go to bed soon.” • These two statements are explanations, not arguments • An argument attempts to establish the truth of a proposition by presenting reasons and an explanation takes the truth of a proposition for granted • To detect an argument you must be able to identify a conclusion (what is being argued for) and the premises (support for that conclusion)

17. Deductive Arguments • Deductive arguments are either valid or invalid • A valid deductive argument is an argument in which the conclusion is logically entailed in the premises • Logical entailment occurs when the conclusion must be true, given that the premises are true • An invalid deductive argument is one in which an argument is offered as valid but the conclusion turns out to not be entailed in the premises • So the premise can be true and the conclusion false

18. Deductive Arguments (cont) • Deductive arguments are frequently presented in the form of a syllogysm • A three line argument in which the first two lines are the premises and the third line is the conclusion • P1: All men are mortal. • P2: Socrates is a man • C: Therefore, Socrates is mortal. • Here is an example of an invalid argument • P1: A stone is a substance • P2: You are a substance • C: You are a stone.