Logic - Syllogisms

General concepts

The truth of contingent statements depends on what exists or occurs in the world. (Look the word 'contingent' up in your dictionary).
The truths of reason, necessary truths, are true in this world and in all possible worlds.

Logic is the study of valid reasoning.

Valid/invalid are judgements about the form of an argument.

True/false are judgements made about the content/language of an argument.

A sound argument is both valid and true.

Deductive arguments reason from the general to the specific, while inductive arguments reason from a collection of particulars to a generalization.

Deductive arguments forms are called syllogisms: categorical, hypothetical, disjunctive.

Syllogisms
General structure:	Premise 1, a conditional statement Premise 2, a fact related to it Conclusion
Categorical syllogism:	All people with red hair get freckles in the sun. Dorrit has red hair Dorrit gets freckles in the sun.
Hypothetical syllogism: p Þ q p q	If a person has red hair then this person gets freckles in the sun. Dorrit is a person with red hair. Dorrit gets freckles in the sun.
Disjunctive syllogism: -p Ú q p q	(At least one of the following alternatives are true:) A person does not have red hair or this person gets freckles in the sun. Dorrit is a person with red hair. Dorrit gets freckles in the sun.

Exercise 1
From the TOK, Teachers Guide, 1989

Which of these syllogisms are categorical, hypothetical, disjunctive?
Which of these syllogisms are valid (V) and which are invalid (inV)?

1.	All men are mortal. Socrates is a man. Socrates is mortal.	2.	All men are mortal. Socrates is mortal. Socrates is a man.
3.	All Communists support socialized medicin. He supports socialized medicine. He is a Communist.	4.	If she goes on a diet, then she will lose weight. And she lost weight. So, she went on a diet.
5.	If she goes on a diet, then she will lose weight. And she went on a diet. So, she lost weight.	6.	If I take the poison, then I will die. But I didn't die. So, didn't take the poison.
7.	If he likes me, then he will call me. And he called me. So, he likes me.	8.	If he does not like me, then he will not call me. He called me. So, he likes me.
9.	If she loves me, then she will marry me. She doesn't love me. She won't marry me.	10.	If it snows, then my car won't start. My car started. Thus, it didn't snow.
11.	If it snows, then school will be closed. It didn't snow. So, the school will not be closed.	12.	(Either) it didn't snow or the school will be closed. It did snow. The scholl will be closed.
13.	(Either) she will cook or I will starve. She didn't cook. I starved	14.	(Either) she will cook or I will starve. She cooked. So, I didn't starve

Exercise 2

Which of these hypothetical types of syllogisms are valid (V) and which are invalid (inV)?
Which type (a,b,c,d,e,f) are each of the examples in exercise 1?

p Þ q
p
q

p Þ q
q
p

p Þ q
~p
~q

p Þ q
~q
~p

p Ú q
~p
q

p Ú q
p
~q