LOGICAL PHYSICS

by Ron Legendario
Logical physics

CHAPTER TWO

THE SPECIAL THEORY OF INFERENCE AND TERMS

3. INDIVIDUALS


The subject-term that cannot be generic with respect to an arbitrary term will be called individual, while the objects denoted by them, the individuals. In other words, a subject-term a is individual if and only if for any term b the following is valid: if b—^a, then a-±b. Examples of individual terms: 'the first astronaut, having performed an orbital flight around the Earth', 'a Russian poet M. Yu. Lermontov, killed in a duel in 1841', 'a planet of the Solar system, Earth', etc. Let a and b be the variables for subject-terms. The above definition may be given the following form: b represents an individual term if and only if It follows from the definition: if a is an individual term, and b-^a, then a-^b and a^±-b. The number of objects denoted by the individual term equals one; therefore these terms are also called unitary. But this characteristic is extra-logical, not promising from the point of view of obtaining logical conclusions. We shall call the variables for individual terms, individual variables. We shall use such expressions as 'An individual d and 'a is an individual'. The first of them is but a linguistic transformation of the term 'An object, denoted by the individual term a\ The second one is a linguistic transformation of the statement 'A term a is individual'. On the other hand, the expression 'individual' itself (as a subject-term) coincides with the term 'object'. When it is used with a specific meaning, it is done with the intention to stress the irreproducible nature of the object. But regardless of our explanation, logical rigor here depends only on reference to the individual quality of the term. Whether we say 'An individual a', 'a is an individual', 'Consider an individual a\ 'Let a be an individual', etc., the exact meaning of all these statements will be the same: a is an individual term, in other words, for any term b, if ft—^a, then a-^b. In addition to the rule provided by the definition, for individual terms the following rules are valid: if a is an individual term, then (1) (2) (3a)xhx. Thus, for individual terms quantifiers are superfluous.