Logic & Philosophy of Language 2-3

THE MAGIC FIVE: SPECIES, GENUS, DIFFERENCE, PROPERTY, ACCIDENT

DEFINITION

Why do we need to define terms?

• Correct communication and correct thinking require clear ideas.
• Clear ideas require knowing both the comprehension and extension of the idea.
• Recall: The comprehension gives us information about the attributes, implications, content of the idea. The extension shows us which things the idea can be applied to.
• To have this clarity of ideas, we need both DEFINITION and DIVISION (discussed in the next section below).

Define 'definition'.

• A definition is a statement which explains what a thing is.
• This implies knowing the comprehension of the term.
• But knowing the comprehension of the term means knowing the thing itself.
• That means careful observation.
• Unfortunately, we cannot know the thing itself fully.
• Our definitions are inadequate.
• In fact, there are some things we cannot define at all, though we might be able to describe them.
• The inadequacy of our definitions leads us to distinguish between different kinds of definition.

So tell me about these kinds of definition.

What are the qualities of a good definition?

1. It must be clearer than the thing defined.
2. It must not contain the idea to be defined. Otherwise, it becomes a circular definition.
3. It must be convertible with the idea defined.
4. It must be positive, not negative, whenever possible. In the case of privations, negative definitions are correctly employed.

DIVISION

What is division?

• Division is the logical operation by which a genus is subdivided into its species. OR (so as not to repeat the word 'divide'), it is the logical operation in which the whole is resolved into its parts. :-)
• In the sciences, this is called classification.
• Every division is always made according to a certain criterion or basis or foundation.

What are the kinds of division?

What are the qualities of a good division?

1. It should be adequate, i.e., all the parts taken together must equal the whole.
   1. No part may be omitted.
   2. No member of the division may equal or exceed the whole.
   3. No member may include the other.
2. It should be clear.
   1. It should be orderly, without jumping from a higher to a lower class and omitting a middle class.
   2. It should be reasonably limited in members.

OPPOSITION OF CONCEPTS

What is opposition of concepts?

• OPPOSITION is the mutual incompatibility between concepts.
• Mutually opposed concepts signify attributes which cannot inhere in the same subject at the same time.

What are the kinds of opposition?

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First Edition. Macao, 9 January 2007