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
Argument
Proof
Premise
Conclusion
A Priori
analytic
Deductive
A posteriori
synthetic
inductive
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.

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... Or to put more simply....
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 premises which are propositions taken 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. A proof is made up of P + P = C
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. A wife is a married woman
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. The two types of proof are….
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.

13. Here are two a posteriori arguments
Here are two a posteriori arguments. What is the difference between them?
Mary wears a ring on the third finger of her left hand
Married women wear rings on this finger
Mary is a married woman
Mary wears a ring
Married women wear rings
Mary is a married woman
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. Can the existence of God be a logically necessary conclusion?
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 ( 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 Bs premise 2: no Bs are Cs conclusion: so no As are Cs
Premise 1: some Fs are Gs premise 2: all Gs are Hs conclusion: so some Fs are Hs

20. Premise 1: all As are Bs premise 2: no Bs are Cs conclusion: so no As are Cs

21. Premise 1: some Fs are Gs premise 2: all Gs are Hs conclusion: so some Fs are Hs

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. Weaknesses of proofs 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.

24. You must develop these ideas further!
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.