To divide a term into its kinds we must regard it in an extensional sense; e. g., the term man may be divided into Caucasian, Mongolian, Malay, Ethiopian, American Indian.

To define a term we must regard it in an intensional sense; e. g., man is a rational animal.

Etymologically considered extension means to stretch out, intension, to stretch within. To use a term extensionally one must look out. To use a term intensionally one must look in.

In attempting to use a term in extension we may ask ourselves the question, “What are the kinds?” or “To what objects may the term be applied?” While if we would use a term in intension the question should be, “What does it mean?” or “What are the qualities?” Let us, for example, use the term metal in the two senses, first in extension, second in intension. Question: To what objects may the term metal be applied? Answer: Metal may be applied to the objects silver, gold and iron. Thus has metal been employed in extension.

Question: What are the qualities of metal? Answer: The qualities are element, metallic lustre, good conductor of heat and electricity. Thus has metal been used in intension.

NOTE. Since an attribute is anything which belongs to a subject, then the parts of a subject must be classed as attributes. Hence, a term is used intensionally when reference is made to its parts.

4. A LIST OF CONNOTATIVE TERMS USED IN EXTENSION AND INTENSION.

The Term.Extensional Use. Intensional Use.
tree.maple, oak, beech.roots, branches, trunk.
or
woody-fiber, sap, bark.
house.stone, brick, cement. foundation, frame-work, roof.
dog.shepherd, fox terrier, bull. carnivorous, quadruped, propensity to bark.
book. textbook, dictionary, encyclopaedia. cover, leaves, binding.
quadrilateral. trapezium, trapezoid, parallelogram. four sides, four angles, limited plane.
logic. theoretical logic, applied logic, educational logic. science of thinking, art of right thinking, treats of laws of thought.
star.Sirius, Arcturus, Vega. heavenly body, gives light and heat, twinkles.
force. gravitation, molecular, atomic.produces motion
changes motion
destroys motion.
term.general, singular, non-connotative. word or group of words, definite idea.
government. monarchy, aristocracy, democracy. body of people, established form of law, banded together for mutual protection.
bird.crow, robin, pigeon. biped, feathered, winged.

5. OTHER FORMS OF EXPRESSION FOR EXTENSION AND INTENSION.

Extension.Intension.
comprehensioncontent
extentintent
breadthdepth
denotationconnotation
applicationimplication