Translating from Ordinary Language

While being able to distinguish valid from invalid categorical argument forms is a remarkable skill, there certainly is reason to question its value if it is not related to real-life language; and real-life talk is not composed of A's, B's, and C's. Of course, some real-life examples have been given above but they have all been straightforward and the fact is that natural languages are much more complex. Indeed, varying contexts, nuances, emphases, idioms, linguistic memes, etc., sometimes make the task of rendering ordinary speech into the statement forms of categorical logic very daunting. Straightforward statements like "All dogs are animals," or even "All pet owners in New York City over 100 years old are millionaires who owe back income taxes," are the exception rather than the norm. Perhaps it can be said that while the determination of validity is a science—indeed, like arithmetic, an exact science—putting ordinary language claims into proper logical form is more of an art that requires judgment. In the final analysis there is no substitute for simply understanding what it is that is being asserted in the ordinary language and then casting it as faithfully as possible into a standard form.

First it should be noted that categorical sentences are simple, having only a quantifier, subject, copula, and predicate; accordingly, compound sentences cannot be put into categorical form. However, sometimes compound sentences can be divided into two or more categorical sentences and often arguments in ordinary language are presented in this manner. For example, the argument:

could be presented as:

or even as:

But not all compound sentences can be divided into simple, categorical sentences like these. Rather, those containing such logical constants as "both/and," "either/or," "if/then," "if and only if," and "it is not the case that" typically cannot be so divided and, accordingly, these fall outside the realm of categorical logic.

However, many sentences that may not appear to be categorical on first glance can nevertheless be rendered so without a loss of meaning, and this is frequently necessary in order to understand and assess the arguments containing them. But this is not to suggest that they should be spoken in standard categorical form; rather, the point is that they should be thought of this way. That is to say, they should be conceived as having a quantifier, subject term, copula, and predicate term in order to understand how the schematics represent them. (Incidentally, they have to be conceived this way for any of the traditional methods of assessing categorical arguments as well.)

I mention some common deviations from standard form below and give the usual ways of handling them.

Whole Sentences

Most sentences beginning with "It is not the case that…" are not categorical; however, since "All A are B" and "Some A are not B" contradict each other, as do "No A are B" and "Some A are B," the denial of any one of these is equivalent to the assertion of its contradiction. Accordingly,

However, the nonstandard form, "All A are not B," is ambiguous in ordinary language, for it is sometimes used to mean "All A are nonB" (as in "All dogs are not cats") while it is also used to mean "Some A are not B" (as in "All dogs are not poodles.") If the conversation is about poodles, dogs, and cats one may feel sure of what the speaker means, but in other settings it may not be so easy to judge.

Quantifiers and Subjects

Often categorical quantifiers are easily identified from their common sense expressions. For example, since "some" means "at least one" it is clear that several, many, most, a few, all but a few, etc., are properly handled as "some." Similarly, "all" is often expressed by each, every, and any as well by such subject modifiers as totally, categorically, universally, without exception, etc. Also, "No" is sometimes expressed by none, nary, not any and zero.

However, all but and none but [= only] are a little more involved. For example, "All but seniors are invited guests" translates as "All nonseniors are invited guests" and sometimes it is used to mean additionally "No seniors are invited guests." (Of course, the question in translating is not "What does the sentence really mean?" but rather, "What does the speaker mean by uttering it?")

On the other hand, "None but seniors are invited guests" translates as "All invited guests are seniors." That is,

There is another oddity with expressions that refer to specific persons, places, times, or occurrences because they typically have no quantifier in ordinary language. Although it may seem a bit strange at first, they are appropriately handled as affirmative or negative universals; that is, to refer to a specific item is to refer to the entire membership of the class of those things that are identical with that specific item. For example, to say "Socrates is mortal" is to say "All members of the class of things identical to Socrates are mortal." Of course, this class has only one member in it, namely, Socrates himself. Accordingly,

Other ordinary language cases have no quantifier and one must decide the quantity by understanding what the speaker means in the given context. For example, "People are homo sapiens" would ordinarily mean "All people are homo sapiens" while "People are still in the building" would mean "Some people are still in the building."

In addition, sometimes subject terms take an article adjective instead of a quantifier and here again the translator must determine the quantity from the meaning and the context. For example, in a natural science class "The elephant is a pachyderm" or "An elephant is a pachyderm" would rightly be taken as "All elephants are pachyderms" while at the zoo "The elephant is from India" would mean "All animals identical with this particular elephant are from India." On the other hand, "An elephant has escaped" would refer to at least one (=some) elephant.

The subject term for logic is usually the grammatical subject of the ordinary language along with all its modifiers except for the quantifier. For example, the subject term of "All adult African elephants in the wild are endangered" is "adult African elephants in the wild." However, as was mentioned above, an exception is that "none but [= only]" takes the "all" quantifier but reverses the translated order of the grammatical subject and predicate.

Furthermore, there are some ordinary language subjects that are combined with their quantifiers and must be divided for the translation. These include the following:

Copulas and Predicates

Although a copula is always a verb of being, it is often singular and in the past or future tense in ordinary language; however, its standard form in logic is always the plural, present tense "are" or "are not." That is, the copula is never "is (not)" since a singular subject in ordinary language (like "Socrates") is handled as a specific instance of a grammatically plural subject in logic. And it is never "was (not)" or "will (not) be" since tense is always considered to be part of the predicate. Accordingly, the ordinary language statement, "Socrates was a philosopher" becomes "All [persons identical to Socrates] are [persons who were philosophers]." Again, this is not to recommend that we actually speak in these awkward-sounding phrases, but rather that we realize such is the theoretical translation necessary to get "All S are P" for the logic.

Other common sentences have no copula at all. In these cases, the copula is inserted and the ordinary language verb is made part of the predicate term. Typical examples are:

Or, instead of saying "animal that swim, bite, jump, or fly" it could be more convenient to say "swimmers, biters, jumpers, or fliers."

When ordinary sentences have "are" as the copula, the predicate term in logic is the grammatical predicate noun with all its modifiers. For example, in "Some birds are animals that cannot fly" the predicate term is "animals that cannot fly." However, quite often ordinary language completes its categorical sentences with adjectives and in these cases the substantive must be added, as follows:

Arguments

Certainly making arguments is not the most common usage of language. Rather we pass information along, narrate stories, tell jokes, etc., much more frequently than we make arguments. Instead, we make arguments only in those instances when we try to prove that something is the case. Accordingly, to inspect an argument we must separate it from any wider discourse in which it may be embedded or intertwined. For example the argument contained in:

is simply:

The additional phrases, though perhaps relevant to the conversation, are extraneous to the argument. Moreover, in some presentations the extraneous material may dominate as the speaker may recite poetry, give examples, or follow side topics between the components of the argument.

Furthermore, while each "term" is used twice in every categorical argument it may be that the very same "word" does not actually occur twice; rather a word and its synonym—or a near synonym— may be used to convey the common meaning instead. In these cases, the synonyms must be collapsed into one term—or into one term and its complement—to achieve proper form for its schematic. For example, the argument given above might have been presented as:

since dogs and canines are (near) synonyms as are beasts and animals. (Of course determining which words have meanings close enough to be collapsed as synonyms is a matter of judgment.)

In addition, ordinary language allows the expression of an argument's sentences in any order. Although perhaps to understand an argument is naturally to understand which sentences are the premises and which is the conclusion, still it may be helpful to note that expressions like therefore, so, hence, thus, consequently, accordingly, it follows that, etc., always introduce the conclusion, while expressions like since, because, for, in that, given that, as, etc., introduce one or more premises. For example, we might give the very same argument in any of the following ways:

Finally, in ordinary conversation we often leave unsaid anything we think "goes without saying." For example, we might argue:

since we feel sure everyone knows that all dogs are animals; or we might say:

if we feel everyone already agrees that all poodles are dogs. Even further, sometimes we might just give the premises and leave it up to the listener to draw the obvious conclusion, as in:

But any unexpressed element in an argument has to be made explicit in order for the argument to be evaluated.

Schematics

Although the letter for any term on the schematics can be clicked or tapped and changed for another, their default listing on the ReasonLines app is in alphabetical order from left to right, and the terms used in most of the earlier examples were selected to match. However, in real-life arguments one would likely want to select different letters—like D for dogs, P for poodles, S for all persons identical to Socrates, etc.—and also the premises may not occur in a convenient order. So, the question arises as to the best procedure for schematizing premises when they do not easily fall into place on the app. An example would be the premises below:

One strategy would be to scan the premises for duplicated (or complementary) terms; these would be middle terms, and the two single terms left would be the extreme terms. In this example these extremes turn out to be the W in premise 2 and the nonH in 4. So one could start with the premise containing the nonH extreme and then match up the successive middle terms of F, L, M, Q, and D by laying their schematics to the right in order to arrive at the extreme term of W. Of course, in the process the default A, B, C, D, etc., would have to be changed to H, F, L M, etc. The full succession of terms would then turn out to be:

and the conclusion schematic would be the up-red-x between H and W. On the other hand, one could begin with the W extreme and lay the successive schematics to the left and the result would be the same.

The alternative strategy would be to begin with the schematic for some other premise—perhaps the first one given—and then lay schematics for the remaining premises to the left or right as they fit. Again the result would be the same.