Syllogisms Assignment

and some definitions

 

Deductive arguments reason from general to particular, while inductive arguments reason from particular (or, more precisely, a collection of particulars) to general.  Examples: Here is a deductive argument: Whenever an odd number multiples another odd number the result is also odd (a general statement, or premise) implies (by deduction) that 11 times 9 will give an odd result (a particular result).  Here is an inductive argument:  My math teachers for grades 7, 8, 9, 10 and 11 were all men (a series of particular observations).  I hypothesis (via induction) that all high school math teachers are men.  A good comparison of the different logics can be found here.

A deductive argument is valid if the rules of deductive logic are applied correctly, whether or not the initial general statement or statements (premises) are true.  Example: See the example of a categorical syllogism below for a valid argument based on an untrue general statement (though you may choose to argue..).

A sound argument is both valid in its use of deduction and true in its premises.  Example: see the very bottom of this page for my syllogism of the assignment.

Inductive arguments have less justification, since even true initial statements do not necessarily make for a sound argument.   Example:  3 is prime and odd, 5 is prime and odd, and 7 is prime and odd (all true statements) do not mean that the conclusion all odds are prime is valid.  (Though the conclusion all primes are odd is.)

A syllogisms is a formal kind of deductive argument first discussed by Aristotle.  Syllogisms come in 3 flavors: categorical, hypothetical, disjunctive.  The general structure of a syllogism is as follows:

Premise 1, a conditional (general) statement
Premise 2, a fact related to premise 1        
Conclusion

Categorical syllogisms begin with a general statement (law) that refers to categories (remember what we discussed about analytical propositions).  It then makes a statement about a sub-class of that category and concludes by applying the general rule of the category to the sub-class.  For example: 

All juniors have fleas.
Carlos is a junior.
Carlos has fleas.

Hypothetical syllogisms are similar but begin with a hypothetical statement.  The general form looks like:  If P is true then Q will be true.  P is true.  So, Q is true.

If a student does not hand in any homework they will fail.
Antonia did not hand in any homework. 
Antonia will fail.

Disjunctive syllogisms begin with two general statements, at least one of which must be true.

A student will either study hard or they will fail the test.
Carlos did not study hard. 
Carlos will fail the test.

Assignment
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)?

 

 

 

The assignment above will get you up to a 90%.  If you would like to go for a 100% you should do one of the following additional exercises:

 

1. Exercise 3 from the page here.

or

2. The exercise here.

 

To state this as a syllogism:

 

Either you will do the first 14 syllogisms PLUS one of the additional exercises, or you will get 90% or less.

You only did the first 14 syllogisms.

You will get 90% or less.