Go back to the child who said dog at a mastiff. The name reached further than the room because a name of that sort is made to. It is worth seeing exactly how, because this is where the doctrine of the last two pages starts paying for itself.
Universal and singular
Some words can be said truly of many subjects, and some of only one. Andres draws the line and gives the test:
“Spot is a dog.” “Fido is a dog.” It is possible that both of these statements are true because the word ‘dog’ is a universal. That is, ‘dog’ is one word that can be the predicate for more than one subject.
Fido is singular. It is meant for one dog. Dog is universal, and so is white, and so is animal. Andres notes the pattern: the more universal the word, the more things it names. Animal names Socrates and Fido and a killer whale.
This is what the child had. Not a list of the dogs there are, but a name that stands to many, so that a dog never met is covered by it already. It is tempting to explain that by saying the word is shorthand for a very large collection, and Maritain says plainly why that is the wrong account:
This alone suffices to show that a universal concept is anything but a collection of individuals: It applies to an infinite multitude because it is originally one (in the mind). That which it presents immediately to the mind is not a collection or series of individuals, but the nature realized in each one of them.
The order runs the other way from the shorthand story. The name does not reach many dogs by having been stretched over them one at a time. It reaches many because what it means directly is one, and that one is the nature the dogs share. Maritain calls the second temptation by its name: nominalism confounds the extension of a concept with its resolution into a simple collection of individuals.
Two ways of measuring a concept follow, and they are worth knowing because the practice applications use them. A concept’s comprehension is what it contains — what belongs to being a dog. Its extension is what it applies to — the dogs. As comprehension grows, extension shrinks: animal applies to more things than dog, and says less about each.
The same name, and not the same meaning
The first page of this foundation described an argument that turned on a word nobody would define, where two people were using one sound for two things and calling it a debate. That has a name and a diagnosis.
Andres, following the opening of the Categories, distinguishes three ways a name gets used:
- Univocally, when the things named have the same name and the same account of what they are. Socrates is a man and Plato is a man; man means the same both times.
- Equivocally, when they have the same name and the account differs. Call Socrates a man, and call a statue of Socrates a man, and the word has done two different jobs.
- Denominatively, when a name is taken from another name with the ending changed, and given to whatever has that characteristic. A man is called virtuous from virtue.
The quarrel was equivocation, undiagnosed. Both parties had the sound. Neither had checked whether it carried one account or two. And nothing about the sound itself will tell them, because the sound is the part we assigned. The check has to be made at the level of the concept, which means it has to be made in words, deliberately, by asking what is meant.
This is also why a definition is the work of the first act rather than an academic formality. To define is to state the one account a name is carrying, so that the name can be used the same way twice.
The practice applications drill all of this: the predicables, the categories, division and definition in Ars Syllogistica, and signification and supposition in Ars Grammatica. This page names the distinctions and stops.
On not settling everything here
There is a deeper question standing behind universals, and you may already have felt it. If dog names many dogs by way of one concept, what is the standing of that one? Is it something real, or only something in our minds? If it is real, is it in the dogs, or apart from them?
Those are the three questions Porphyry raises at the opening of the Isagoge, the standard introduction to this material for something like fifteen centuries. Here is what he does with them:
I shall keep away from the deeper questions but shall aim rightly at the simpler, i.e., I shall refuse to say whether genus and species are subsistent or are located only in naked concepts, and if subsistent, whether they are corporeal or incorporeal, and whether separate from sensible or subsisting in them and around them. That business is very deep and requires a greater examination.
He declines, in the first paragraph, and gets on with the work. Andres does the same and says so: these are difficult questions, and we will postpone them until we are further along in philosophy. Maritain, at the corresponding place, sends the formation of the mental word to psychology rather than settling it in a logic.
Take that as the measure for this course as well. Everything on these three pages is settled doctrine, and you need it before you can begin. The question of the inner word, left open on the first of them, is of the other kind, and it is left open by better books than this one. Declining a question at the threshold is not a hole in an introduction. It is how introductions are built, and Porphyry set the precedent.
The tools of the mind
One last thing, to put the three arts in their place before you meet the first of them. Andres compares the mind to the hand.
The hand is a universal tool. It can do nearly anything, and few things well. You can dig with your hands, and fight with them, and it is better to dig with a shovel. So the hand’s real advantage is that it makes tools, and then does those jobs well.
The mind is like that. Left to itself it manages ordinary matters well enough; no one needs logic to learn to fix a car. On harder questions it does poorly unless it makes tools for itself, and the tools it makes are these: words that carry a thought precisely, statements that put words together, arguments that put statements together. Grammar, logic, and rhetoric are the care of those tools.
You now know what the tools are made of. A word, which is ours and conventional and replaceable. A concept, which is not ours and is measured by the thing. A statement, which is where truth becomes possible. The first art is the composing of the first of these into the third.
Continue to Grammar.