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Arguments in Ordinary Language

People reasoning in ordinary language rarely express their arguments in the

restricted patterns allowed in categorical logic. But with just a little revision, it is often

 possible to show that those arguments are in fact equivalent to one of the standard-

form categorical syllogisms whose validity we can so easily determine. Let's consider a few of the methods by means of which we can "translate" ordinary-language

arguments into the forms studied by categorical logic.

Translation into Standard Form

In the simplest case, we may need only to re-arrange the propositions of the

argument in order to translate it into a standard-form categorical syllogism. Thus, for 

example, "Some birds are geese, so some birds are not felines, since no geese are

felines" is just a categorical syllogism stated in the non-standard order minor premise,

conclusion, major premise; all we need to do is put the propositions in the right order,and we have the standard-form syllogism:

No geese are felines.

Some birds are geese.

Therefore, Some birds are not felines.

Reducing Categorical Terms

In slightly more complicated instances, an ordinary argument may deal with more

than three terms, but it may still be possible to restate it as a categorical syllogism.

Two kinds of tools will be helpful in making such a transformation:

First, it is always legitimate to replace one expression with another that means the

same thing. Of course, we need to be perfectly certain in each case that the

expressions are genuinely synonymous. But in many contexts, this is possible: in

ordinary language, "husbands" and "married males" almost always mean the same

thing.

Second, if two of the terms of the argument are complementary, then appropriate

application of theimmediate inferences to one of the propositions in which they occur 

will enable us to reduce the two to a single term. Consider, for example, "No dogs are

non-mammals, and some non-canines are not non-pets, so some non-mammals are

 pets." Replacing the first proposition with its (logically equivalent) obverse,

substituting "dogs" for the synonymous "canines" and taking the contrapositive of the

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second, and applying first conversion and then obversion to the conclusion, we get the

equivalent standard-form categorical syllogism:

All dogs are mammals.

Some pets are not dogs.

Therefore, Some pets are not mammals.The invalidity of this syllogism is more readily apparent than that of the argument

from which it was derived.

Recognizing Categorical Propositions

Of course, the premises and conclusion of an ordinary-language argument may

not be categorical propositions at all; even in this case, it may be possible to translate

the argument into categorical logic. For each of the propositions of which theargument consists, we must discover some categorical proposition that will make the

same assertion.

One especially common but troublesome instance is the occurrence of  singular 

 propositions, such as "Spinoza is a philosopher." Here the subject clearly refers to a

single individual, so if it is to be used as the subject term of a categorical proposition,

we must suppose that it designates a class of things which happens to have exactly

one member. But then the categorical proposition that links Spinoza with the class

designated by the term "philosopher" could be interpreted as an A proposition (All S

are P) or as an I proposition (Some S are P) or as both of these together. In such cases,we should generally interpret the proposition in whichever way is most likely to

transform the argument in which it occurs into a valid syllogism, although that may

sometimes make it less likely that the proposition is true.

Other cases are easier to handle. If the predicate is adjectival, we simply

substantize it as a noun phrase in order to make a categorical proposition: "All

computers are electronic" thus becomes "Some computers are electronic things," for 

example. If the main verb is not copulative, we simply use its participle or incorporate

it into our predicate term: "Some snakes bite" becomes "Some snakes are animals

that bite." If the elements of the categorical proposition have been scrambled, werestore each to its proper position: "Bankers? Friendly people, all" becomes "All

bankers are friendly people." And, in a variety of cases your texbook discusses in

detail, the statements of ordinary language often contain significant clues to their most

likely translations as categorical propositions.

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Remember that in each case, our goal is fairly to represent what is being asserted

as a categorical proposition. To do so, we need only identify the two categorical terms

that designate the classes between which it asserts some relation and then figure out

which of the four possible relationships (A, E, I, or O) best captures the intended

meaning. It is always a good policy to give the proponent the benefit of any doubt,

whenever possible interpreting each proposition both in a way that recommends it aslikely to be true and in a way that tends to make the argument in which it occurs avalid one.

Occasionally these methods are not enough to provide for the translation of 

ordinary-language arguments into standard-form categorical syllogisms. Next, we

examine a few special instances that require a more significant transformation.

Introducing Parameters

In order to achieve the uniform translation of all three propositions contained in acategorical syllogism, it is sometimes useful to modify each of the terms employed in

an ordinary-language argument by stating it in terms of a general domain or 

 parameter. The goal here, as always, is faithfully to represent the intended meaning of 

each of the offered propositions, while at the same time bringing it into conformity

with the others, making it possible to restate the whole as a standard-form syllogism.

The key to the procedure is to think of an approriate parameter by relation to

which each of the three categorical terms can be defined. Thus, for example, in the

argument, "The attic must be on fire, since it's full of smoke, and where there's smoke,

there's fire," the crucial parameter is location or place. If we suppose the terms of thisargument to be "places where fire is," "places where smoke is," and "places that

are the attic," then by applying our other techniques of restatement and re-

arrangement, we can arrive at the syllogism:

All places where smoke is are places where

fire is.

All places that are the attic are places where

smoke is.

Therefore, All places that are the attic are places where

fire is.

This standard-form categorical syllogism of the form AAA-1 is clearly valid.

Enthymemes

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Another special case occurs when one or more of the propositions in a categorical

syllogism is left unstated. Incomplete arguments of this sort, called enthymemes are

said to be "first-," "second-," or "third-order," depending upon whether they are

missing their major premise, minor premise, or conclusion respectively. In order to

show that an enthymeme corresponds to a valid categorical syllogism, we need only

supply the missing premise in each case.

Thus, for example, "Since some hawks have sharp beaks, some birds have sharp

 beaks" is a second-order enthymeme, and once a plausible substitute is provided for 

its missing minor premise ("All hawks are birds"), it will become the valid IAI-

3 syllogism:

Some hawks are sharp-beaked animals.

All hawks are birds.

Therefore, Some birds are sharp-beaked animals.

Sorites

Finally, the pattern of ordinary-language argumentation known as sorites involves

several categorical syllogisms linked together. The conclusion of one syllogism serves

as one of the premises for another syllogism, whose conclusion may serve as one of 

the premises for another, and so on. In any such case, of course, the whole procedure

will comprise a valid inference so long as each of the connected syllogisms is itself valid.

Sorites most commonly occur in enthymematic form, with the doubly-used

 proposition left entirely unstated. In order to reconstruct an argument of this form, we

need to identify the premises of an initial syllogism, fill in as its missing conclusion a

categorical proposition that legitimately follows from those premises, and then apply

it as a premise in another syllogism. When all of the underlying structure has been

revealed, we can test each of the syllogisms involved to determine the validity of the

whole.

Understanding how these common patterns of reasoning can be re-interpreted as

categorical syllogisms may help you to see why generations of logicians regarded

categorical logic as a fairly complete treatment of valid inference. Modern logicians,

however, developed a much more powerful symbolic system, capable of representing

everything that categorical logic covers and much more in addition.

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