I am writing up a piece for myself as I have no idea where it could be published. But I am willing to share it with anyone interested. It is just a pice of criticism of a lecture I have found on the net on Definitions.
1. The defintion of defintion
When a definition is to be defined to arrive at a definition all you do is to say this (semantic analysis):
Facet 1 – sense 1, word class verb, operation
Definition is a verb (to define, a relation), (usually) a concept (object) tagged by a word (definition, object) serving as a shorthand and looking as a noun.
Facet 2 – sense 2, word class noun, operand
The operation defining in the definition form results in another object, a cluster of words called defintion (another object, the words with which you define).
Facet 3 – sense 3 word class noun, operand
What (object called subject that may not be made explicit) you define by using a definition (operation) is another object either existing or not. Such an existence may mean that the object is already tagged (has a name) or it is not, it is an object that is at least visually observable or somewhat tangible to your senses or to be identified for your own mind. Therefore definition may be an operation to defined objects not verbally, but using other visual obejcts. Such an operation may be different from giving a verbal defintion,.nevertheless the same brain with the same operating capacities are used, therefore the algorithm must have some common elements in them.
Now it is a common mistake to forget about our change of view (rotation) in our mind as a result of which we see either form or content and instead we misrelate them. In a lengthy exercise on defintion by Norman Swartz, Simon Fraser University http://www.sfu.ca/philosophy/ the author says (Under 2.1, near the end) “For example, the term, "pain", is defined, but pain itself is not defined. We define only terms, never their referents.”
(end of sampling my text)
Later he says: Any teaching that a certain word is the name for a certain thing should be called "definition". (, pp. 48-49)
Dictionaries are not designed to adjudicate such issues or to settle whether or not a given policy is "democratic". Scholars and thinkers write volumes on such matters.
My comments: a word IS a name itself and the definition of that word is both about the object and its name. It depends on what sort of word is, like is it a noun, a verb or an adjective each calling for a different definition subject to whether the thing is real (existing) or not. Would it not be for a single word, then the boundary between a dictionary and a lexicon would be removed.
When we use the name of a term in accordance with the just-reported convention we are said to be mentioning the term. We mention a term, by using its name.
My comment: (The distinction between use and mention is not clear to me. To mention means to use it in speech or in writing)
Since a term is a word or an _expression_ used for a particular thing, a term is used as a name of that thing. It is not clear if that particular thing is an object in real life or a concept (term=concept?), but clearly a term IS a name in use by mentioning it in speech or writing.
When we form the names of terms by quoting them, we form their names iconographically. We literally picture them.
Quoting is mentioning in quotes to indicate that the word or _expression_ (term) is the name of a concept or an object, where a concept is also an object as to be detailed later. When we picture this concept iconographically we mean to say that the word(name) is also associated with the picture of the real thing in the mind. In other words there is a non verbal imagery associated with the concept and its verbal representation (name).
This convention we have in English of forming the name of a term by the device of enclosing that term within quotation marks is just that, a convention.
This is not really necessary. A word is a form or a name of an object, the content of which are its properties.
The use/mention distinction (as it has come to be called) is of particular relevance in the theory of definitions. For when we give the definition of a term, we mention the term, we do not use it.
What he is saying here, that memtioning a term as in a definition is not considered to be use. I protest: this mentioning IS use for the purpose of clarification, and as an alternative form to be used for and in place of the term in question.
For example, the term, "pain", is defined, but pain itself is not defined. We define only terms, never their referents.
The term (name) of pain as defined above is not completely defined, hence incomplete, meaningless. We do define the referents though, like it is an object, namely feeling with properties such as hurting, unbearable, felt for duration and at a location, etc. Notice that the properties listed are of different kind: unbearable could be rewritten as the level of pain, duration as lasting or short, etc.
If the object is a concept, or an intangible object (internally identified) like pain above, then the defintion should be the feeling in the body of being hurt somehow.
 ▸ noun: a word or _expression_ used for some particular thing
("He learned many medical terms")
Quotation marks, as we have just seen in the previous section, create new names. In general, substitution is not permitted within quotation marks.
This does not make sense to me, because it only says that a name (a phrase in quotes) should not be changed, which should be obvious.
To circumvent this problem, mathematicians and logicians have invented a special-duty set of quotation marks - " " and " " - sometimes called "quasi-quotes" and sometimes called "corner-quotes". Corner-quotes act pretty much like ordinary quotation marks except that they do allow substitution in their midst. To
capture the intention of the rule discussed above, one would write:
If P and Q are formulas, then (P & Q) is a formula.
All that above is superfluous in my eyes.