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"Survey Ship," NOAA, theb0115.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.

  1. 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.

    1. 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.

    2. Translation Rules of Thumb:

      1. Rule 1: The subject and predicate terms must be the names of classes.

        1. If the predicate term is a descriptive phrase, make it a substantive (i.e., noun phrase).

        2. Translation must not (significantly) alter the original meaning of the sentence.

        3. E.g. “The ice all around was green as emerald” can translate as

          “All surrounding ice is something green as emerald.”

      2. Rule 2: Categorical propositions should have a form of the verb “to be” as the copula in the present tense.[1]

        E.g. see the translation of the statement about “ice” just above.

      3. Rule 3: The quality and quantity indicators are set up from the meaning of the sentences.

        1. Quantity indicators: "All," "No," "Some."

        2. Quality indicators: "No," "are," "are not."

        3. 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.

          1. 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.”

          2. 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.”

      4. 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.

    3. Rule 4: The word order is rearranged according to the sense of the sentence.

      1. This rule requires special care—in some instances, it may well be the most difficult rule to follow.

      2. On occasion, we might need to divide one sentence into two or more propositions.

    4. Before we take up some special cases, let's look at some typical examples.[2] The following translations are relatively straightforward.

      1. “Ships are beautiful” translates to
        “All ships are beautiful things.”

      2. “The whale is a mammal” translates to
        “All whales are mammals.”

      3. “Whoever is a child is silly” translates to
        “All children are silly creatures.”

      4. "Snakes coil" translates to
        “All snakes are coiling things.”

      5. “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.”

    5. 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."

 

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: 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.


  1. The following types of statements deserve special mention.

    1. 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.

    2. 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.”

    3. Exceptive propositions are compound propositions.

      1. E.g., “All except A is B” translates to
        “All non-A is Band “No A is B.”

      2. 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.”)

    4. 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.”


    5. The translation of many statement forms depends upon context. E.g., the proper translation of statements of the form

      “All S is not Por
      “Not every S is P

      can have several different forms depending upon the occasion:

      1. 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.”

      2. 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.[3]

      3. 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

1. The rule of restricting the copula to some form of the verb “to be” helps minimize errors of equivocation of tenses in the translation; however, many textbooks do not use this rule.

2. I owe many of the examples on this page to the clear and skillfully written introductory logic textbook by Thomas S. Vernon and Lowell A. Nissen, Reflective Thinking (Belmont, CA: Wadsworth Pub. Co. 1968). LCA

3. Again, context is the key. Where a statement of the form “All S is not P” is not obviously meant as an E proposition (e.g. it is not a statement like “All squares are not curved figures”), it is sometimes identified as the “Sneaky O proposition” even though it might entail the truth of its corresponding I statement as well as well as the O.. See F.F. Centore, “The ‘Sneaky O’ Proposition,” The New Scholasticism 44 no. 4 (Autumn, 1970), 600-602, and a rejoinder Theodore E. James, “Humpty Dumpty and the ‘Sneaky O’ Proposition, ” The New Scholasticism 45 no. 4 (Autumn, 1971), 590–599.

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