AMBIGUOUS STATEMENTS

Finally, once more on the ambiguity of natural language and the importance of context. Consider the statement:

Some doctors have bad handwriting.

As it stands this is a simple !-statement.

Here as before, we shall not try to guess at such conversational implications. When we are asked to symbolize a statement, we will symbolize what we are given. If a natural argument depends on such an implication, however, then we shall have to make explicit such implicit features. That said, there are some statements in English that are genuinely ambiguous even as they stand. The worst culprits are statements of this form:

(1) All PLANETS are not LIFELESS.

What does this mean? It could mean

(2) No PLANETS are LIFELESS.

or it could mean

(3) Not all PLANETS are LIFELESS.

i. e., by the square of opposition,

(4) Some PLANETS are not LIFELESS.

Statement (2) is an E-statement, whereas (4) is an Î-statement. They mean different things. If someone said (1) to you, you would have to ask which she meant, (2) or (4). Consequently, we should try to avoid statements of the form (1), not just in a logic course, but generally, if we want to be understood.

SUMMARY

• In Aristotelian logic, each statement is a categorical statement, that is one that asserts a connection between two categories or terms, the subject term and the predicate term.

• A categorical syllogism is an argument consisting in two premises and a conclusion (all categorical statements), in which each term appears in the argument twice.

• The four main types of categorical statements are

À-statement: All A are B. !-statement: Some A are B. E-statement: No A are B. Î-statement: Some A are not B.

• À-statements and O-statements are contradictories. So are !-statements and E-statements.

EXERCISES 15.1

1. Identify whether each of the following statements is an A-, E-, I-, or O-statement:

(a) Dolphins are mammals.

(b) Many accountants have a sense of humour.

(c) No place in the world is empty.

(d) Some jokes are lost on him.

(e) Weaners suck.

2. Put the following statements in standard form, and identify whether each is an A-, E-,

I-, or Î-statement: e.g., (a) No G are W.—E-statement:

(a) GOURMETS don’t eat their steaks WELL-done.

(b) Each TABLET contains 15 mg of CAFFEINE.

(c) There are airline PILOTS who have an ALCOHOL problem.

(d) Anybody who RACES horses must BELIEVE in miracles.

(e) The Vatican GUARDS are all SWISS.

(f) Not everyone who TRAINS WINS.

(g) Many BIRDS fly at HIGH altitudes.

(h) He who DEFILES an Egyptian tomb will PERISH.

(i) Not many ANIMALS cannot be TAMED.

(j) EXCEPTIONS must be MADE.

(k) NOBODY is PERFECT.

15.2