18 ottobre 2007

II lesson of classical logic: the term

Term (from Latin terminus - limit, border), in logic it is the pole of beginning and the pole of end of a sentence: subject and predicate are the poles of the logical sentence. The term can be calls word, apprehension (what is learned), concept (because conceived by the mind), idea. It can be expressed by an only word (a), with an epithet (b), with a circumlocution (c), enriched by an apposition not influential in the logical function (d).
Examples:
(a) B. Franklin.
(b) Great inventor.
(c) Who invented the lightning-rod.
(d) B. Franklin, great inventor that operated in the 18° century.

To observe that in all these cases, the term is only one: Benjamin Franklin.

The terms in the proposition can be represented by a segment of line, where the initial sign and the final sign identify the two correspondent terms: subject → predicate.
In what way we come to quantify the subject:
The subject can be universal (a), particular (b), singular (c).
(a) All the dolphins;
(b) Some dolphin;
(c) That dolphin there.

Regarding the universal term and the particular term we needs to keep in mind that the definite article is enough to make the quantity of the subject: to say "all the dolphins", "every dolphin" or, simply "the dolphins" is, in effects, entirely equivalent; while, the indefinite article "a", is enough to give a particular connotation to the word. So, to say "some dolphin", "some dolphins" or "a dolphin" is the same thing.

Comprehension and extension.
The comprehension is the complex of the notes that individualize a subject. When I say "man", I imply these notes of individualization: being, living, sentient, reasoning. Instead, the extension is the whole of the individuals referable to the same term: when I say "man", I imply, practically, all the inhabitants of the planet. Now we have to fix a fundamental rule in which the extension and the comprehension are correlated.

Quo maior comprehentio, eo minor extentio.
So much big is the comprehension, so much small is the extension.
Quo maior extentio, eo minor comprehentio.
So much big is the extension, so much small is the comprehension.

Let us make an example: the men are around 6 million, the living (really because this category also embraces the animals and the plants) are million of million. It is based on the principle that much more the subject is specified, much more the possibility is reduced to be applied to others.

In what way the verbal predicate can be resolved in a nominal predicate.
This operation is useful to better identify the second term of the proposition.
The dolphins live the seas = The dolphins are inhabitants of the sea.

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