variablemathematics and logic

The variables here serve as placeholders for terms or names. Thus, replacing “α” by “substance,” “β” by “animal,” and “γ” by “dog” in the schema yields: “If every animal is a substance and every dog is an animal, then every dog is a substance,” a syllogism in Barbara. Aristotle’s logic was a...

...inference form. The letters—X, Y, and Z—in (3) mark the places into which expressions of a certain type may be inserted. Symbols used for this purpose are known as variables; their use is analogous to that of the x in algebra, which marks the place into which a numeral can be inserted. An instance of an inference form is produced by replacing all the...

Frege’s work represents the beginning of modern logic because of his invention of the notation of quantifiers and variables. (In natural language, generality is represented by inserting an expression like “everything” or “something” in the argument-place of the predicate; in the notation used in logic since Frege, the argument-place is filled by a variable letter, say...

...the function symbols for “successor,” “S,” and for arithmetical addition and multiplication, “+” and “ · ”; constants 0, 1; and variables x, y, z, . . . .The following are terms: a constant is a term; a variable is a term; if a is a term, Sa is a term; and, if a and b...

...thing”—namely, that everything is ϕ—and (∃x)ϕx and (∃y)ϕy both mean simply that something is ϕ. Clearly, so long as the same variable occurs both in the quantifier and as the argument of ϕ, it does not matter what letter is chosen for this purpose. The procedure of replacing some variable in a quantifier, together with...

Viète introduced the concept of algebraic variable, which he denoted using a capital vowel (A, E, I, O, U), as well as the concept of parameter (an unspecified constant quantity), denoted by a capital consonant (B, C, D, and so on). In his system the equation...

To formulate an operations research problem, a suitable measure of performance must be devised, various possible courses of action defined (that is, controlled variables and the constraints upon them), and relevant uncontrolled variables identified. To devise a measure of performance, objectives are identified and defined, and then quantified. If objectives cannot be quantified or expressed in...

...suppose that a particular study is interested in characteristics such as age, gender, marital status, and annual income for a sample of 100 individuals. These characteristics would be called the variables of the study, and data values for each of the variables would be associated with each individual. Thus, the data values of 28, male, single, and $30,000 would be recorded for a 28-year-old...