Logic: Apprehension and Terms
Apprehension is the act of understanding an idea. For a child, this may be learning what a cat or a unicorn is, and for an adult it may be learning what a double integral is. This act of the mind leads to an idea, a concept of the thing that one apprehends. One of the main differences of Aristotelian philosophy is that it argues that these concepts actually correspond to the forms of things, how things actually are. An idea may represented by a term, which is merely a verbal representation of an idea. It is conceivable that the word cat could have come to mean the concept of a dog and vice versa.
Jolivet adds that “terms can … include multiple words (for example, the good God, certain men, a brilliant action), that do not however form a single logical idea”. (CdF) What he is trying to say is that when we say that a man is good and a food is good, good is meant in two different ways; in the first, it means that a man is virtuous, but in the second it means that the food is delicious. “Good” is still one term but is used ambiguously, as we will later explain.
An idea can viewed from the point of view of comprehension and extension. Comprehension refers to what an idea actually means. For instance, a triangle is comprehended by the definition “a closed, 2-dimensional shape with 3 straight sides”. A triangle drawn in a moving car may have curved, irregular sides, but, viewed from the point of comprehension, that does not mean that it is not a triangle, it just means that there are defects in the construction (the “matter”) of the triangle and it just does not live up too well to the definition. Extension refers to all the instances that an idea corresponds to. In the case of the triangle, this could refer to all the instances of triangles in the world. Kreeft says that this is the way that most people today conceive of ideas, which can lead to some absurd conclusions.
For instance, the fact that there are badly drawn triangles does not mean that we need a new definition in order to encompass those badly drawn triangles; there is a material defect which makes those triangles not correspond as well to the form of triangle. Similarly, simply because some people are born with ambiguous genitalia mean that they form a new sex category or that the “old” categories of male and female are incorrect — it just means that there is a material defect (chromosomal abnormality, exposure to chemicals, etc) that stops them from actuating the form (male or female) that they were supposed to be.
Jolivet points out that “comprehension of an idea is in an inverse relationship with its extension”. (CdF) What this means is that a simple concept, such as “animal”, has a massive extension, but a small comprehension (e.g the concept is not very complex). But a more complex concept, such as “rational animal”, has narrowed the extension to humans, but broadened its comprehension.
Additionally, Jolivet introduces the traditional Aristotelian notions of genus and species. Genus he describes as the “superior idea in regards to extension”, and species as the “inferior [in extension] in regards to the former”. (CdF) Simply put, this means that the genus of an idea will always have a greater extension than the species. For instance, the genus of man is “animal” and his species is “man”. Animal will always have greater extension than man, and for that reason it is the genus. Jolivet further explains: “In principle, an idea that contains itself other general ideas (animal in relation to man, birds, fish, etc) is called genus, and species all ideas that only contain anything except individuals”. (CdF)
Classification of Ideas and Terms
Jolivet divides ideas into three categories in order to explain the difference between them. Kreeft adds several more. I picked the most useful of Kreeft’s classes and placed them at the end, since, strictly speaking, they are not classifications of ideas or terms, but instead a result of the (often bad) uses of terms.
“From the point of view of the perfection of the idea”
Jolivet distinguishes between adequate/inadequate, clear/unclear, and exact/vague aspects of an idea:
An idea is adequate when it represents in spirit all the elements of the object. It is inadequate in the opposite case.
An idea is clear when you can recognize the object from all others; and unclear in the opposite case.
Kreeft explains this very well: “The term ‘quasar’ is clear to those who know modern astronomy but not to those who do not”. (SL)
Back to Jolivet:
An idea is distinct or confused [Jolivet’s term for exact and vague, respectively] when it allows us to know or not to know the elements of which it is composed. A clear idea can be confused: A gardiner has a clear, but not distinct, idea … of the flowers which he cultivates. On the other hand, a distinct idea is necessarily clear.
Jolivet juxtaposes the gardiner to the botanist, who knows all the parts of the flower and therefore has an exact idea of what the plant is. The gardiner’s idea of the flower is clear — he can distinguish it from others — but he has not the expertise of finding out the exact parts of the plant, such as the functions and morphology of its organs, etc.
“From the point of view of the idea’s comprehension and extension”
With regards to comprehension, an idea is either “simple or complex, based on whether it comprehends one or many elements. The idea of being (that which is) is simple; the idea of man (rational animal) is complex.” (CdF)
There are three types of terms from the point of view of extension: singular, particular, and universal. (CdF)
A singular idea refers to one individual. Plato, that book, this pen.
A particular idea is “applied indeterminately to only one part of a species or to a determined class. Some ducks.” (CdF) In the term “some ducks”, it is applied indeterminately, since it is unknown how one is distinguishing the ducks. In the term “green ducks”, it is clear what class of ducks one is referring to.
A universal idea “includes all individuals of a genus or a given species: [all] men, [all] circles”. (CdF) Jolivet points out that the singular case is a special case of the universal idea, since “it is limited to a single individual, it exhausts its extension”. (CdF)
“From the point of view of the idea’s relationships with other ideas”
Traditionally, there exists the distinction between contradictories and contrary ideas. Contradictories are when one idea excludes another. (Cdf) For instance, “being and non-being; being on the moon and not being on the moon”. (CdF) Contraries are when an intermediate point can be defined between two ideas: “black or white; avaricious and prodigal; being in Bilbao or being in Pamplona”. (CdF)
The reason why being on the moon and not being on the moon are contradictories whereas being in Bilbao or being in Pamplona are contraries lies in the definition of the idea. One is either on the moon or not on the moon — there is no intermediate state of superposition where one is both on the moon and not on the moon. Location-wise, even if you are between earth and the moon, you are not on the moon, you are in space. In contrast, whereas one is either on the moon or not on the moon, one can be in other places than Bilbao or Pamplona: one can be in Madrid, or Kansas City, which are intermediates to the ideas of being in Bilbao or Pamplona.
Ambiguity
Kreeft defines ambiguity as “‘having more than one meaning’. Strictly speaking no term is ambiguous unless it is used ambiguously.” (SL) For instance, I can say that a man is good and a meal is good, but, whereas the former means virtuous and capable, the latter means tasty and nutritious. “But a good man is not tasty and nourishing, except to a cannibal”. (SL) This is the problem of ambiguity, but there is a very way to fix it: “Defining a term”. (SL)
Univocal, Equivocal, and Analogical Uses of Terms
Terms are either univocal, equivocal, or analogical. A univocal term has one and only one meaning. An equivocal term has two or more quite different and unrelated meanings. An analogical term has two or more meanings that are (a) partly the same and partly different, and (b) related to each other. (SL)
When the term “capybara” is used in the statements: “I pet a capybara” and “I saw a capybara”, it is used univocally, since it only has one meaning. When a pirate marks “X” on a map and when I send “Xs and Os” to my loved ones, “X” is used equivocally. In the former, “X” represents buried treasure, but in the latter it represents a kiss. When I call an eraser a “rubber” and the material used for making tyres “rubber”, I use “rubber” equivocally, for the “rubber” of an eraser is not the same as the “rubber” of a tyre.
Definition of Terms
Definition of Definition
“Logical definition consists of, in effect, exactly circumscribing the comprehension of an object; in other words, saying what a thing is.” (CdF)
When defining something you describe only the comprehension of a thing, and you make no judgment on whether it exists or not. A definition is saying what an idea is, and contains no judgment on whether the idea exists in reality or not. I may come up with the idea of pigs that can fly, which in fact contains no judgment on whether pigs fly or not, but merely contains an idea. The only time a judgment can be made that does not exist solely based on the idea of it is in the case of contradictory ideas. The famous cases here are the round square, or the triangle with four sides. Since, by definition, squares cannot be round and triangles cannot have four sides, we can safely assume that they do not exist. In fact, many philosophical controversies are due to contradictory definitions, or at the very least misunderstanding of them.
Types of Division
Jolivet distinguishes between two types of division: nominal and real. Nominal definitions refer to what a word means. “To say that the word ‘to define’ means ‘to delimit’ is to give a nominal definition.” (CdF)
“The real definition expresses the nature of a thing.” (CdF) This is in fact an extreme claim compared to what most modern philosophy teaches. If you recall, modern philosophy teaches that the real nature of things are unknowable and that words and definitions are just shorthand that the human mind uses to not get overwhelmed by the amount of information. Aristotle rejects this and states that reality is (a) intelligible to the human mind, and (b) that the definitions of things actually encapsulate what things are.
Jolivet says that there are two types of real definitions: essential and descriptive.
The essential definition is the most precise and “real” of these definitions because it describes a thing’s essence; that is, what it actually is. It is performed by finding the “closest genus and the specific difference. We can define man in this way: rational animal; animal is the closest genus, which is to say the idea immediately superior in terms of extension to man; and rational is the specific difference, which is to say the quality which, added to a genus, constitutes a species distinct from all the other species of the same genus.” (CdF)
The descriptive definition “enumerates the most distinguishing external characteristics of a thing in order to distinguish them from all the others. (The ram is a ruminant with an elongated face, stooped nostrils, sluggish eye) This definition is used in the natural sciences.” Jolivet says that this definition is used when an essential definition is lacking, which makes sense in the natural sciences. When one is first investigating something, say an electron, one possesses no notion of what it is. The charge, the size, the mass of an electron may be known, but this is sufficient only to distinguish it from other things. Absent a complete theory of physics, the essence of an electron will remain unknown, and only experimental data describing what an electron is will give us its definition.
How to Divide Ideas
Definition of Division
Jolivet defines division as “distributing a whole into its parts” (CdF). Division is performed for further study of an idea. Kreeft further notes that division is performed across “the extension of a term” (SL).
Types of Wholes
Jolivet defines a whole as “anything that can be divided, whether physically or at least conceptually, into its elements”; there are three classes of wholes: “physical, logical, and moral”. (CdF)
Physical wholes are made of parts which “are really distinct”. Jolivet distinguishes between physical wholes that are "quantitative, where it is composed of homogenous parts: a block of marble; essential, when the whole forms a complete essence: man; potential, where it is composed of different faculties: the human soul since it is composed of intellect and will; accidental, when composed of parts that are united accidentally: a table, a pile of rocks.” (CdF)
There are also metaphysical wholes, whose “parts cannot be distinguished except by reason”. (CdF) A metaphysical whole is a “universal notion who contains in itself other subjective parts. It is this way that the genus contains the species. [an example is] the idea of animal in reference to the rational animal (man) and the irrational animal (brute).” (CdF)
Finally, there are moral wholes, “whose parts, although actually distinct and separated, are united by the moral tie of the same end: a nation, an army, a family, etc.” (CdF) Jolivet states that moral wholes always refer to a collective.
Rules of Division
For a division to be a good division, it must be exclusive, exhaustive, and possess only one basis for division. (SL)
Jolivet defines exclusivity as follows: “it should not enumerate elements except those that are really distinct from each other.” (CdF) Kreeft gives an example: “Dividing political systems into monarchical, constitutional, and democratic violates this rule because a regime could be both monarchical and constitutional, as well as both democratic and constitutional.” (SL)
Exhaustiveness is defined as a: “complete or adequate [division], which is to say that it enumerates all the elements of which it is composed of.”(CdF) Again, Kreeft gives a good example: “Dividing the term ‘meat’ into beef and lamb violates this rule because it omits pork1.”(SL)
The division should have only one basis because “it should proceed from members which are really opposed to each other. The following division: my library is composed of books of philosophy and books with good spines, would go against this rule, since having a good spine is not opposed to philosophy”. (CdF)
And poultry, game, etc!