The Problem of Ordinary Language In Syllogistic Reasoning:
Mastery of standard form, categorical, syllogistic, reasoning would solve most problems in formulating valid arguments if everyone thought, spoke and wrote in standard categorical forms. Since this is seldom the case, several problems arise when trying to convert statement claims into standard form categorical propositions for syllogistic analysis and reasoning. Without resolving these special problems of ordinary language translation, skill in syllogistic reason is of very little practical use in a life of ideas, a debate with other minds, or a search for new knowledge.
In formulating your term paper main argument and any supporting arguments you may find it relatively easy to state your case in ordinary language, but somewhat awkward to formulate that same argument in a valid standard form categorical syllogism in one of the 15 forms you now master. Therefore, as you begin your term paper syllogism, some guidelines are now offered to help you translate form ordinary language into standard form categorical logic.
Many logic and critical thinking textbooks offer a set of "rules" or "techniques" and "guidelines" for serious thinkers and writers to resolve these problems easily. The strategies presented here are adapted from the most common suggestions to make categorically explicit the logical entailments found in most ordinary language. Later in this course we will present 19 rules of natural deduction that offer even greater precision for this task as they render propositional logic in symbolic formulae.
These guidelines below are by no means exhaustive on this topic, but they do provide a set of necessary starting conditions for students determined to employ categorical reasoning.
Clever students will notice that the overarching axiom in all these rules, techniques, or strategies is the axiom of EXPLICITNESS, i.e. formulating propositions that express EXACTLY what you mean, not a little more, not a little less.
1. Singular Propositions:
In ordinary language, claims often take the form "Arnold Schwarzenegger, the movie actor, is a Governor of the State of California." This propositional claim is an example of a 'singular proposition' It claims that there exists at least one entity named Arnold Schwarzenegger, the movie actor, and that this entity, Arnold Schwarzenegger, the movie actor is a member of the category called, Governors of the State of California. Since this particular category, Schwarzenegger, the movie actor, has only one member, then it is a 'singular' claim, and so, easily translates into a Type I standard form categorical proposition, Some things that are members of the category Arnold Schwarzenegger, the movie actor, are members of the category Governors of the State of California. Notice that as a Type I proposition, there may be, as a matter of factual truth, only one member of the category Arnold Schwarzenegger, the movie actor. But that satisfies the existential import of any Type I proposition, since in logic 'some' means 'at least one'. This may seem to be torturing the language tediously and for no practical purpose, but such is not the case.
By precisely this sort of translation from ordinary language into exacting standard form categorical language, an exhaustively clear meaning of the proposition emerges eliminating all vagary and/or ambiguity if this proposition is used as a premise or conclusion in formal argument. This is seen when apply conversion to the original ordinary language proposition with the resulting: "A Governor of the State of California is Arnold Schwarzenegger."
What then are students to make of the passage:
"Provided that we keep in mind the existential import of singular propositions....it is acceptable practice to regard singular propositions as universal (A or E) propositions."
All that is meant is simply this. Concerning ALL members of the category Arnold Schwarzenegger, the movie actor, are members of the category, Governors of the State of California. Since this particular category, Schwarzenegger, the movie actor has only one member, whatever is said about that one member can be said about ALL members of that category. Therefore, categories with only one member can be translated into both universal and particular proposition, if and only if, the singular membership of that category is explicitly expressed.
2. Adjectives And Adjectival Phrases Translated to Nouns:
Often, ordinary language propositions use adjectives or adjectival phrases to express attributes of a category. But since attributes determine a category connotatively, then they are easily translated into categorical nouns. The claim that, All wars are immoral, has an adjective as it's predicate yet is easily translated into All wars are immoral actions.
And the expression in ordinary language, Some news is not fit to print, easily translates into a standard form Type O proposition, Some news items are not items that are fit to print. Again, explicit categorical expression results in the full logical content revealed when translated into standard form categorical propositions.
3. Verbs Other Than the Verb "To Be":
Statements in ordinary language such as some teens surf the web for hours are simply missing a part of the verb 'to be' in order to translate them into standard form. By supplying the copula 'are' the translation is quickly made to some teens are teens that surf the web for hours. And by a combination of translating techniques the ordinary language expression, everyone wants happiness, becomes a standard form Type A proposition, all people are those that want happiness.
An important thing to remember is to keep the tense of the verb consistent in both premises and conclusion.
Thus, the ordinary language statements like the following offer no hope of translation into a valid standard form categorical syllogism: Everyone lies about sex. My husband lied about sex. Therefore, my husband will lie about sex. The first premise translates to All people are those that LIE about sex. The second premise introduces, some people, MY HUSBAND being at least one of them, are people that HAVE LIED about sex. And the conclusion claims because of these premises, Therefore, some people, my husband being at least one of them, are people who WILL LIE about sex. There are FIVE different categorical terms here; all people, my husband, those people that lie about sex now, those people that have lied about sex in the past, and those people that will lie about sex in the future. This six term confusion is caused by a shift in the tense of the verb "to be".
4. Simple Re-arrangement of Standard Form Ingredients:
"All's well that ends well." is a popular aphorism from ordinary language taken from Shakespeare. By simple re-arrangement it translates into the standard form Type A, all things that end well are things that are well. Thus, by explicit categorical language, all the necessary components of any standard form categorical proposition are supplied.
5. Translating Quantifiers:
One of the most vexing problems of ordinary language statements is the problem presented by quantifiers other than the standard ALL, NO, and SOME. How do quantifiers like, most, many, the majority, almost every, nearly all, not every, with few exceptions, only, none but, translate into ALL, NO, or SOME as required by standard form? Care must be taken here. Affirmative propositions are not too much trouble since anything shy of all translates to SOME (at least one, maybe many, maybe most, maybe nearly all). All means just that, all, and not a single exception. But a word of caution.
How do you translate the ordinary language proposition, "Only war is evil."? If you think it translates as, "All war is evil." then think again. The claim states that concerning the entire membership of the category 'evil' it has but one member and that member is 'war'. Therefore, "All evil is war." becomes the correct way to translate the original claim into a standard form Type A proposition. This is where your knowledge of conversion, obversion and contraposition comes in handy.
6. Exclusive Propositions:
However, many ordinary language negative propositions do offer some special difficulties. Propositions such as, not every post-modernist is a clear thinker, or not any post-modernist is a clear thinker translate quite differently into standard form. The standard form meaning of not every post-modernist is a clear thinker is some post-modernists are not clear thinkers. Whereas, the standard form meaning of not any post-modernist is a clear thinker is no post-modernist is a clear thinker. And the propositions only clear thinkers are logicians, or none but clear thinkers are logicians both translate into all logicians are clear thinkers.
7. Propositions With No Quantifiers:
Context may be the only clue to determine the quantity implied by ordinary language propositions. Were someone to enter a room and utter the claim, "Children are present" few if any reasonable people would think that this statement implied that; "All children are present". Clearly the context determines the implied quantity here. But in the case of a similar proposition "Children are serious responsibilities" no reasonable person would think that this statement implied only "Some children are serious responsibilities." Once more, explicit use of language in standard form categorical propositions will eliminate any ambiguity about how many are referred to by propositions with no quantifiers. Rhetorical flare my impel us to drop quantifies as in "The good die young." Logical validity, however, requires that we explicate rather than presume. If we mean all, then say so. If not, then use some.
8. Propositions That Merely Resemble Standard Form:
With the preceding strategies mastered, it should be simple to translate some ordinary language statements that resemble standard form, but need a bit more explication in order to do so.
"Not all Republicans are Conservatives" translates into "Some Republicans are not Conservatives"
"Nothing triangular is four-sided" translates into "No triangles are four-sided figures"
"There are alien beings" translates into "Some beings are alien beings"
9. Exceptive Propositions:
Most difficult of all ordinary language propositions to translate into standard form are those that claim exceptions to some general rule or attribute. The reason for this stems from the fact that propositions claiming a universal, but with some exceptions are literally claiming two things at the same time. It is therefore necessary to explicate precisely what the two claims actually are by means of two translation into two separate standard form categorical propositions. In the event that an exceptive proposition is used as a premise in an ordinary language syllogism, then two separate standard form syllogism are required to autopsy the exact meaning and validity of the argument. Here's how that works.
Take the ordinary language proposition "All but slobs are welcome to attend my party." This asserts two independent claims. 1. "All non-slobs are welcome to attend my party." and 2. "No slobs are welcome to attend my party." The set of things 'slobs' and the set of things 'those welcome to attend my party' are complementary sets.
Now suppose "All but slobs are welcome to attend my party." is used as a premise in an ordinary language syllogism.
Everyone who is welcome to attended my party is properly dressed.
All but slobs are welcome to attend my party.
Therefore, some slobs are not properly dressed.
To check the validity of this ordinary language syllogism the premises must be translated into standard form. The first premise translates easily to: All who are welcome to attend my party are properly dressed persons. The second premise has two translations. Taking the first we get: All non-slobs are welcome to attend my party. Therefore, All non-slobs are properly dressed persons. This is a Valid AAA-1 Barbara If we take the second translation of the second premise we get: no slobs are welcome to attend my party. Therefore, some slobs are not properly dressed. This is an Invalid AEO-1
However, since one of the translations of the second premise from the ordinary language syllogism does yield a VALID translation, then the ordinary language argument is in fact valid for that translation, and invalid otherwise.
Note: should an ordinary language argument be formulated with two standard form categorical propositions and an exceptive proposition as its conclusion, no hope of valid translation exists. The reason is that the premises can not validly entail more than one meaning at the same time. Since exceptive propositions functioning as a conclusion do precisely that, no validity can be established.
Useful Quote (The idea about TV news distortion of truth):
"... is to keep everything brief, not to strain the attention of anyone, but instead to provide constant stimulation through variety, novelty, action and movement...bite-sized is best, that complexity must be avoided, that nuances are dispensable, that quantification impedes the simple message, and that visual precision is an anachronism."
~ Robert MacNiel, Executive Editor and co-anchor of the MacNeil-Lehrer News Hour, Public Broadcasting Service (PBS)