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 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 well know, people do not use
standard categorical form. Categorical form is much too stilted for
effective discourse and becomes complex when translating nuanced
expressions.
- Nevertheless, in order to assertain the validity of many ordinary
language arguments, accurate translation into standard form categorical
propositions is essential for testing validity. Occasionally translation
into standard form reveals fallacies of equivocation or
amphiboly in the original text. A translation must preserve the literal
of logical significance of the original statement.
- Translation Rules of Thumb:
- Rule 1: 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.
- E.g. “The ice all around was green
as emerald” can translate as
“All surrounding ice is something green as
emerald.”
- Rule 2: Categorical propositions should have a form of
the verb “to be” as the copula in the present
tense.
E.g. see the translation of the statement about
“ice” just above.
- Rule 3: 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."
- Whenever a statement is expressed indefinitely without a
quantity indicator, some logic textbooks advise to treat them
as universal statements. However, it is best to judge
from the context of the subject-matter as to whether or
not the statement should be translated as universal or
particular.
- E.g., the statement “People are mortal”
would normally judged to be universal …
“All people are mortals,”
whereas “People are poets” would normally be judged
to be particular …
“Some people are poets.”
- However, in the context of a religious or spiritual
discussion of persons having the possibility of eternal
life, the former statement “People are mortal”
might be taken as particular, namely …
“Some people are mortals,”
and in the context of a psychological discussion of innate
formative abilities as expressed in potential behaviors, the
latter statement might justifiably be taken as
universal:
“All people are poets.”
- So a precise interpretation of quantifiably
indefinite statements can be obtained through the
application of the
principle of charity,
a practice whereby the translation is logically consistent
with other ideas expressed in the passage being
interpreted or being analyzed.
- Rule 4: 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 might 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.”
- “Nothing ventured, nothing gained” translates to
“No non-ventured things are gained things.”
Or can be translated by
obversion into
“All non-ventured things are non-gained things.”
- More complex examples sometimes can be “mechanized”
in a translation process consisting of applying the steps
listed above as ”Rules of Thumb“ in a effective
fashion.
| (1) "When the cat's away, the mice
will play."
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| Rule 1 |
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times when the cat is away |
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times when the mice will play |
| Rule 2 |
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are |
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| Rule 3 |
All |
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| Rule 4 |
~not applicable~ |
| (2) "It is not uncommon for a
musician to have perfect pitch"
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| Rule 1 |
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musicians |
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people with perfect pitch. |
| Rule 2 |
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are |
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| Rule 3 |
Some |
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| Rule 4 |
~not applicable~ |
| (3) "None but the brave
deserve the fair."
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| Rule 1 |
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brave people |
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people who deserve the fair. |
| Rule 2 |
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are |
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| Rule 3 |
All |
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(but this is not the meaning!) |
| Rule 4 |
All people who deserve the fair are
brave people. |
Clarification: Example #3 is an exclusive proposition.
Consider another 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 non-symbolic
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 times to sow” and
“Some occasions are times to reap.”
- The translation of many statement forms depends upon context. E.g.,
the proper translation of statements of the form
“All S is not P” or
“Not every S is P”
can have several different forms depending upon the occasion:
- The translation is “No S is P”
when the context makes it clear that the S and P classes
are understood to be exclusive (i.e., completely different).
E.g., when speaking to a child “All triangles
are not four-sided figures.” would normally signify “No
triangles are four-sided figures.”
- Other times, when the context makes clear that there are exceptions
to the generalization, the minimal translation would be “Some
S is not P.” E.g., speaking to a child
while viewing white swans at the zoo, the statement
“All swans are not white” would normally be
interpreted to mean “Some swans are not white,”
a statement pointing out that some swans are of a different color
that those being now observed. This case has been designated as the
“sneaky O proposition.
- Finally, there are occasions where “No S is P” means
both subcontraries. E.g., the statement “All human
beings are not ethical agents“ would normally be interpreted to signify
both of the following statements:
“Some human beings are not ethical agents” and
“Some human beings are ethical agents”
Notes
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