|
|
|
 Philosophy
103: Introduction to Logic
Translation of Propositions
Abstract: Some well-known techniques
for translating ordinary language sentences into standard form
categorical propositions are explained.
- For reasoning in everyday life, as you know, people do not talk in
standard categorical form. Categorical form is much too stilted for
writing effective discourse.
- There is a need to develop skills of logical translation to
standard form categorical propositions in order to minimize errors
in evaluating syllogistic arguments. Very often translation into
standard form reveals fallacies of equivocation and fallacies of
amphiboly in the original text.
- Translation Rules of Thumb:
- The subject and predicate terms must be the names of classes.
- If the predicate term is a descriptive phrase, make it a
substantive (i.e., noun phrase).
- Translation must not (significantly) alter the original
meaning of the sentence.
- Categorical propositions must have a form of the verb "to be"
as the copula in the present tense.
- The quality and quantity indicators are set up from the meaning
of the sentences.
- Quantity indicators: "All," "No," "Some."
- Quality indicators: "No," "are," "are not."
- The word order is rearranged according to the sense of the
sentence.
- This rule requires special care—in some instances,
it may well be the most difficult rule to follow
- On occasion, we need to divide one sentence into two or
more propositions
- Before we take up some special cases, let's look at some typical
examples:
- The following translations are relatively straightforward.
- "Ships are beautiful" translates to
"All ships are beautiful things."
- "The whale is a mammal" translates to
"All whales are mammals."
- "Whoever is a child is silly" translates to
"All children are silly creatures."
- "Snakes coil" translates to
"All snakes are coiling things."
- "All swans are not white" translates to
"Some swans are not white."
- "Nothing ventured, nothing gained" translates to
"No non-ventured things are gained things."
Or the obverse...
"All non-ventured things are non-gained things."
- More complex examples can be "mechanized" in a translation process consisting of applying the above "Rules of Thumb" in a effective fashion.
| (1) "When the cat's away, the mice
will play."
|
| Rule 1 |
|
times when the cat is away |
|
times when the mice will play |
| Rule 2 |
|
|
are |
|
| Rule 3 |
All |
|
|
|
| Rule 4 |
~not applicable~ |
| (2) "It is not uncommon for a
musician to have perfect pitch"
|
| Rule 1 |
|
musicians |
|
people with perfect pitch. |
| Rule 2 |
|
|
are |
|
| Rule 3 |
Some |
|
|
|
| Rule 4 |
~not applicable~ |
| (3) "None but the brave
deserve the fair."
|
| Rule 1 |
|
brave people |
|
people who deserve the fair. |
| Rule 2 |
|
|
are |
|
| Rule 3 |
All |
|
|
(but this is not the meaning!) |
| Rule 4 |
All people who deserve the fair are
brave people. |
Clarification: This example is an exclusive proposition. Consider
this further example:
"None but black things are crows" is another way of
saying "All crows are black things."
Hence, when translating exclusive
propositions to standard form, the subject and predicate classes are
usually reversed.
- The following types of statements deserve special mention.
- Singular propositions are to be treated as (but not usually translated into) a universal proposition (i.e., an A or an E).
E.g., "Socrates is a man" is an A proposition, but
"Socrates is not a god" is an E proposition.
- Exclusive propositions have the cue words "only" or "none but." The order of the subject and predicate terms must be reversed.
E.g., "None but A is B" translates to "All B is A."
"Only A is B" translates to "All B is A."
"None but red trucks are fire engines" translates to
"All fire engines are red things."
- Exceptive propositions are compound propositions.
- E.g., "All except A is B" translates to "All non-A is B
and "No A is B.
- E.g., "All except human beings are nonsymbolic animals" translates to ..."
"All nonhuman beings are nonsymbolic animals" and
"No human beings are nonsymbolic animals"
(or, of course the obverse, "All human beings are symbolic animals.")
- A Compound statement asserts two propositions.
E.g., "There is a time to sow and a time to reap" translates to
"Some occasions are timse to sow" and
"Some occasions are times to reap."
|
|
