In logical discourse “term” (terminus in Latin, meaning limit, boundary) is used to refer to the opening and closing particles of a logical sequence having meaning and hence called a statement or proposition. Subject and predicate are the two terms of any logical proposition. A term may be equally a word, an apprehension (in the sense of something grasped mentally, understood), a concept (in the sense of something conceived mentally), or an idea. As such a term may be instantiated by: (a) a single word; (b) an epithet; (c) a circumlocution; (d) a noun phrase by way of an apposition to the term itself that in any case does not affect the term’s logical function being merely an explanatory equivalent of the term, or a complementary specification entailing an extended but irrelevant proposition within the discourse.
Here are four examples:
(a) Garibaldi.
(b) The hero of the two worlds.
(c) He who lead the expedition of the thousand.
(d) The general who wore a red shirt and about whose exploits there are varying and contrasting opinions.
Whatever the form, then, the term is always the same, which in our example is “Garibaldi”.
A graphically effective way of representing the terms of any proposition is the segment of a straight line as shown below, where the perpendicular cut-off lines at the two ends mark its initial and end terms, that is its subject and its predicate.
Lets now take a closer look at the subject. Firstly, lets see how it can be quantified. Again, we are confronted with three alternatives. The subject may in fact be: (a) universal; (b) particular; (c) singular.
Here are three examples:
(a) All dolphins.
(b) Some dolphins.
(c) That dolphin there.
A universal term may be quantified by omitting any article in front of the subject: “all dolphins” or “every dolphin” are in fact equivalent to “dolphins”. Use of the indefinite article “a” or the partitive “of the” in front of the subject renders it particular; “some dolphins” or “of the dolphins” are in fact equivalent.
Comprehension and extension
All the specific features by which any individual may be identified go to make up comprehensiveness as referred to that individual. “Man”, for instance, is implicitly typified as being [an] “entity”, “animate”, “cognizant”, and “rational”.
Extension, instead, refers to the full set of individuals that may be included under the same term. Leaving aside gender bias, “man”, for instance, is often used to include all human inhabitants of the Earth. Lets now formulate a basic rule to help us understand how comprehension and extension are inversely related to each other:
Quo maior comprehentio, eo minor extentio.
The greater the comprehension [of a term] the less [its] extension.
Quo maior extentio, eo minor comprehentio.
The greater the extension [of a term] the less [its] comprehension.
This rule may be easily verified by applying it to our example. If we consider all the individuals that may qualify as “man”, then there are about six billion to account for, while if we consider what may be classified as “animate”, there are billions of billions (all animals and plants) to be accounted for. The underlying principle at work here is of course that the more an individual is characterized the less are the possibilities of finding individuals having the same characteristics.
A verbal predicate may be changed to a nominal predicate.
This operation comes in handy for better identifying the second term of a proposition.
Here’s an example:
Dolphins live in the sea = Dolphins are denizens of the sea.
Nessun commento:
Posta un commento