A Class-Room Introduction to Logic

May 4, 2009

Unit-VI: Translating Sentences into Standard form Propositions

Filed under: Logic,Translation to Standars form proposition — Dr. Desh Raj Sirswal @ 8:44 am

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.
1.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 careā€”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.”

2. 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.
3. 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.”

4. 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.”)

5. A Compound statement asserts two propositions.
E.g., “There is a time to sow and a time to reap” translates to
“Some occasions are times to sow” and
“Some occasions are times to reap.”

6. Abstract: An inductive strategy for mechanizing translation is illustrated.

We have at this time a kind of “took kit” to work on syllogisms. Our tools include:
obversion, conversion, and contraposition
Venn diagrams
logical analogies
rules and fallacies
various techniques for reducing the number of terms
translation strategies

The following inductive technique can be used for mechanizing translation by isolating the steps for testing the validity of a syllogism. The steps can be itemized as follows:

Identify the conclusion and premises.

Put the syllogism into standard order as best you can.

Supply the suppressed statements, if any.

Reduce the number of terms to three per syllogism.

Translate the statements to standard form.

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