Abbreviate Definition to D, Intension to IN and Extension to EN (eg IND = Intensional Definition).

I desire to, but I am unsure whether I should, abridge my long quote; feel free to emend my post.
Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick J. Hurley

[p 92:] The previous section of this chapter explored the cognitive meaning of language in general. The cognitive meaning of terms comprises two kinds: intensional and extensional. The intensional meaning, or intension, consists of the qualities or attributes that the term connotes, and the extensional meaning, or extension, consists of the members of the class that the term denotes. For example, the intensional meaning of the term “cat” consists of the attributes of being furry, of having four legs, of moving in a certain way, of emitting certain sounds, and so on, while the extensional meaning consists of cats themselves—all the cats in the universe. The term connotes the attributes and denotes the cats.

[p 106:] Although it is conceivable that extensional definitions could also serve as techniques for theoretical and persuasive definitions (though this would be highly unusual),

[1.] extensional definitions by themselves cannot properly serve as precising definitions for the following reason.

The function of a precising definition is to clarify a vague word, and vagueness is a problem affecting intensional meaning. Because the intension is imprecise, the extension is indefinite. To attempt to render the intension precise by exactly specifying the extension (as with an extensional definition) would be tantamount to

[2.] having extension determine intension—which cannot be done.

The principle that intension determines extension, whereas the converse is not true, underlies the fact that

[3.] all extensional definitions suffer serious deficiencies.

For example, in the case of the demonstrative definition of the word “chair,” if all the chairs pointed to are made of wood, observers might get the idea that “chair” means “wood” instead of something to sit on. Similarly, they might get the idea that “Washington Monument” means “tall” or “pointed” or any of a number of other things. From the definition of “actress,” readers or listeners might think that “actress” means “woman”— which would include countless individuals who have nothing to do with the stage or screen. From the definition of “tree” they might get the idea that “tree” means “firmly planted in the ground,” which would also include the pilings of a building. And they

[p 107:] might think that “cetacean” means “aquatic animal,” which includes salmon, tuna, squid, manatees, and so on. In other words, it makes no difference how many individuals or subclasses are named in an extensional definition, there is no assurance that listeners or readers will get the intensional meaning. Extensions can suggest intensions, but they cannot determine them.

I do not understand the grey above, but do understand all else.

[4.] Why can only IND determine END? Eg: an IND for a cat may not resolve unclear and vague cases; eg, some strange felid hybrid may match all your attributes, but may still not be a cat.

[5.] Why cannot END determine IND? 3 implies that only END suffer serious deficiencies, but to me, END appears equally effective as IND? For example, detailed information (eg: physical evidence, pictures, videos) of 95% of all cats may inform more about cats than any IND.

2 Answers 2


1) An intensional meaning picks out a set of things in the world, giving the corresponding extensional interpretation. But the world changes, e.g., new cats are born every minute. So the derived extensional definition of cat would almost always be incomplete. An extensional equivalent to the definition of 'cat' would therefore just not be equivalent.

2) Any set of real objects has more attributes in common than you can list. The list of people on your soccer team may also have in common a sex, a national origin, fit into different ranges of heights, or weights, or hair colors, or blood pressure readings... Many combinations of those traits may be sufficient to select just that set of beings. There are too many possibilities for selecting out that exact set of people to guess that the relevant aspect is playing soccer with you currently. Not knowing which sets of parameters matter, you cannot stop adding options, because you do not know what kind of seemingly irrelevant detail might have been part of the intended interpretation.

3) This is just not true, the extensional definition of something like the number 3 = {2, 1, 0} in mathematical logic is just fine. It is uncommon in the real world that a list of things is really what you intended to consider, but it happens. For instance, you can probably list all the different kinds of commercial recording media in existence in 1972 and have a useful extensional definition with relevant applications in historical domains. Your author is strangely biased.

4) If something meets all the requirements on the taxonomy to be in a species, that thing is in the species. A given person may have an inadequate stated definition of 'cat', but somewhere, some biologist has one that is absolutely definitive, by the standards of zoology in general. And you can, in theory, therefore check out all the animals in the world and identify only the cats, giving you a (temporary) extensional definition of 'cat'.

5) is just 2) restated.


It seems to me that Hurley's statement amounts to the following.

Example : if we assume that the "concept" cat is vague, this means that we are encountering some individuals that we are not able to decidee if we have to classify them as cats or not.

If so, the extensional approach, i.e. list all the cats in the universe and assume the list as (an extensional) definition of cat will not work, simply because we have "imported" the vagueness into the listing.

Thus, the only way to eliminate the vagueness is to strengthen the criteria for accepting an individual as a cat, in order to "decide" the vague cases, i.e. refining the intensional definition.

Having said that, it does not seem to me that Hurley suggests that "Intensional Definitions are less deficient [compared to Extensional ones]" nor that "vagueness disturb only Intensional Meaning, and not Extensional Meaning".

We can say instead that Hurley argue for the "priority" of Intensional over Extensional.

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