Arguments and Proofs

1. Arguments and Proofs Learning Objective: To explore what a Philosopher means by “argument” and “proof”. Philosophy of language and logic....

2. Keywords for the lesson Tip: start a glossary or keyword list to help you as you are reading and to make sure you include them in your written and verbal responses. • Argument • Proof • Premise • Conclusion • A Priori • analytic • Deductive • A posteriori • synthetic • inductive

3. Think! • Philosophers use arguments to prove things. • So we have two questions: • What is an argument? • What is proof?

4. An Argument • In philosophy when we talk about an argument we don’t mean a row between two people • It’s means the same as when we say you “argue” your point of view. • An alternative word for argument is a proof. • Lets look at some proofs.

5. A Proof Quotes linked with proofs... a proof is that which results from a valid argument constructed from a set of true premises. an argument which starts from one or more premiseswhich are propositionstaken for granted for the purpose of the argument, and argues to a conclusion. (Swinburne) Or to put more simply.... Proof: Any effort, process, or operation designed to establish or discover a fact or truth.

6. The Proof Formula A proof is made up of P + P = C P = a premise. A premise is a statement about something, e.g “Mary is a wife”. C = a conclusion. So… P + P = C Mary is a married woman. Mary is a wife + A wife is a married woman =

7. Beware!Based on incorrect premise • Premise 1: Mary is a wife • Premise 2: all wives are good at ironing • Conclusion: so Mary is good at ironing

8. Beware!Incorrect conclusion • Premise 1: Mary is a wife • Premise 2: all wives are female • Conclusion: so females are called Mary

9. Your Task Come up with three proofs using the formula “P + P = C”.

10. Premise 1: all his friends are rap fans • Premise 2: all rap fans are word-lovers • Conclusion: so all his friends are… • Premise 1: all squares are rectangles • Premise 2 all ….. Are quadrilaterals • Conclusion: so all…. Are quadrilaterals • Premise 1: all ostriches are… • Premise 2: all birds are egg layers • Conclusion : so all …. Are egg layers • Premise 1: all…. Are bops • Premise 2: all bops are… • Conclusion: so are bips are bups • Premise 1: all films shown before 9pm are supposed to be suitable for family viewing • Premise 2: all films that are supposed to be suitable for family viewing are films without violence • Conclusion: so…..

11. Two types of proofs • Look at this proof and explain how it is different from the first example with Mary • Mary wears a ring • Married women wear rings • Mary is a married woman Mary is a wife A wife is a married woman Mary is a married woman

12. A Priori, analytic or deductive Which means..... These arguments are not dependant on experience, but have a logically necessary conclusion. The conclusion offers no new information. A posteriori, synthetic or inductive Which means.... These arguments are based on experience. They come to a conclusion that is probable, but has a chance of not being true. The two types of proof are….

13. Mary wears a ring Married women wear rings Mary is a married woman Mary wears a ring on the third finger of her left hand Married women wear rings on this finger Mary is a married woman Here are two a posteriori arguments. What is the difference between them? They could both be true, but one is more PROBABLE than the other. It is more likely to be true.

14. Tasks • In groups write four a priori arguments, and four a posteriori arguments. • When you have finished number your a posteriori aruguments in order of probability. No 1 is the most likely and No 4 the least likely.

15. Logica card sort game Inductive or deductive???? Strong or weak inductive? Sound or unsound deductive?

16. Deductive proof Can the existence of God be a logically necessary conclusion? A set of premises that move towards a logically necessary conclusion. Does not conclude anything that is not already contained in the original premises (analytic). a priori because the conclusion is not dependent on external evidence or experience (no verification necessary) Do we not need external verification? Is God’s existence self-defining?

17. Inductive proof Should we rely on our experience to verify our assumptions? A set of premises that move towards a conclusion that is not logically necessary, but is only probable. The conclusion of the proof is not contained within the premises (synthetic). a posteriori because the premises and conclusion are dependent on external evidence or experience (they require verification). Is a probable conclusion strong enough evidence to base faith? Is it reasonable?

18. Using Venn diagrams…. • One of the most famous Greek philosophers Aristotle (384-322 BC) actually published some rules of logic that were part of formal education up till the 19th century. • Edward Venn, an English clergyman devised a way of picturing them that made it much easier to understand. (the VENN diagram!)

19. How would you draw the following... • Premise 1: all As are Bspremise 2: no Bs are Csconclusion: so no As are Cs • Premise 1: some Fs are Gspremise 2: all Gs are Hsconclusion: so some Fs are Hs

20. Premise 1: all As are Bspremise 2: no Bs are Csconclusion: so no As are Cs b c a

21. Premise 1: some Fs are Gspremise 2: all Gs are Hsconclusion: so some Fs are Hs f g

22. There are 13 different possible 3 circle combinations in pairs make up a new one and try to bring the diagram to life with an example to fit it

23. Deductive Leads to apparently necessary conclusions – why is this a weakness? Depends on acceptance of the premises being analytically true. Inductive Depends on our acceptance of the nature of the evidence. Demands overwhelmingly good reasons for accepting that the conclusion is the most probable. Alternative conclusion may be just as likely. Weaknesses of proofs

24. Problems of proofs • They are dependent on limited experience and resources. • Believers do not allow anything to count against proofs. • An atheist can legitimately reach different conclusions from those of the theist. • If the existence of God were self evident, there would be no need for proof. You must develop these ideas further!

25. Consider…… • What does it mean to say that God exists? • How would you establish whether it is true to say “Thou shalt not steal”? Do you think the truth of this statement depends on the society in which one lives? • If all the possible checks have been carried out to ensure that a statement is true, is it still possible that the statement could nevertheless be false? • Where did you learn about God? How big an influence do you think parents and background have on the religious beliefs an individual may have.