Example from John Hospers: "An Introduction to Philosophical Analysis", 3th. ed., Routledge, London, 1990.

Consider this argument (from a trial):

• If the guard was not paying attention at the time, the car was not noticed when it came in.
• If the witness's account is correct, the guard was not paying attention at the time.
• Either the car was noticed or Jones is hiding something.
• Jones is not hiding anything.
• Therefore: The witness's account is not correct.

Name the single propositions with letters (p, q, r ...). Transform the compound propositions to symbolic statements. Use the rules of inference (syllogisms) to check if the conclusion ('Therefore: ...') is correct.

In everyday speech, it would be a bit queer to spell everything out, although in a formal demonstration of evidence of an assertion, this is a requirement.

In these everyday statements identify premises and conclusion (or invent them if they are missing). (Common premise indicators are: 'since', 'because', 'for', 'given that', 'in view of'; common conclusion indicators are: 'thus', 'it follows that', 'hence', 'so', 'therefore'.)

1. The defendant is insane, so he is not guilty.

2. That is not a good dictionary, because it does not give the origin of the word.

3. All philosophers are eccentric and Karl is a philosopher.

4. Coffee must contain a stimulant, because it keeps people awake.

5. He is either on this flight or the next one, and he was not on this one.

Find the form (categorical, hypothetical or disjunctive syllogism) and the validity (valid or invalid) of the following arguments:

1. If inflation is allowed to continue, the unions will demand a steep rise in wages. And that is what is going to happen, because inflation is going to be allowed to continue.

2. The alternatives seem to be that the United States government weakens its NATO commitment by withdrawing troops from Europe or that it meets increasing criticism at home for the enormous funds spent in maintaining these troops abroad. The government will never weaken its NATO commitment: so we may expect that criticism to increase.

3. The food in the cafeteria will improve or there will be a student strike. And since there is a student strike scheduled for tomorrow, it follows that the food will improve.

4. The streets are no safer today than they were five years ago; yet if the Crime Control Act was effective, we would expect streets to be safer. Hence, the Act was not effective.

5. Granted that if there were no problems on earth, man should explore the moon. But you admit that there are problems on earth, so man should not be spending money to explore the moon.
(After solving this, look up re Exercise 3 - Beware of traps!)

6. If people disagree about whether human beings descended from lower forms of animals or were specially created, then the textbooks in biology should state explicitly that this question has not been settled by science. They do disagree, and that is what the textbooks should say.

7. Maybe the Governor did accept bribes from the racing syndicate to fix the races, or maybe, on the other hand, these accusations are just vicious rumours spread by his political enemies. The latter I cannot believe, so I conclude that the Governor took the money.

8. By 1985, either we will institute far-reaching procedures to recycle our trash, or by 1985 we will have to find room to dispose of 440 million tons or waste paper, junk cars and plastics that will be produced each year by the affluent society. But we are assured that somehow such room will be found, so large scale recycling will not be necessary.

9. If the French tend to eat, drink, and smoke more than people in other European countries, then we may assume their life-expectancy to be lower than people in, for example, Great Britain, Denmark, Italy, Germany, and this is exactly true. The French men live an average of 67.1 years: women 74.6 years: a good deal lower than other European citizens. The conclusion? The French eat, drink, and smoke too much.

Look for instance at problem '5'. Did you judge it to be invalid? Let us consider it:

p: there are problems on earth (war, hunger, polution etc.)
q: man should explore the moon

Wrong suggestion of syllogism:

~p Þ q
  p       
~q

This syllogism is certaintly invalid. (see types of syllogisms, c).
But it is not the correct representation of the quotation in '5'!

The conditional formulation of '5' ('were') should rather be interpreted as:
"Only if there were no problems on earth, man should explore the moon."

So, 'no problems on earth' is a necessary condition for 'man should explore the moon'.

The correct suggestion of a syllogism must then be:

q Þ ~p
p       
~q

This syllogism is valid. (see types of syllogisms, d).

See also about A sufficient or a necessary conditions.

See also A poem.

Find a short text; it can be a fragment of an article from a newspaper or a magazine or from a novel, shortstory or poem. Make a logical analysis of the text, trying to identify examples of syllogisms, discussing type, validity, missing or hidden parts, symbolic representation etc.