Post by Eugene 2.0 on May 28, 2022 15:11:47 GMT
For a proposition it is true to be either true, or false if it concerns any binary algebra, or else, it has the relevant value to its high: n values in n-high algebra (e.g. 3 values: true, undefined, false in three high algebra).
A proposition can be presented in two ways: a complese sentence, a sentence with quantor. If we've got so no quantor sentence like it's cold, then it can be viewed as p. But in case of quantor in a sentence like the Sun is heating, we've got a quantor so this sentence can be presented as ∃x.Sx&Hx.
If to take an incomplete proposition or a propositional form as x is a traitor, then instead of saying something about it we've got a description of class in which x presents a class of traitors. In other words we might take a class, but we've used a form like x is a traitor to describe it.
This propositional form can be presented as Px, Rxy, and it means x is a pony, x rides y. If x is a horse and y is a horse, then the first and second statements would be: Ph and Rhh so, horse is a pony, which is true, and horse rides a horse which isn't true. But it works only when the substitution is completed. Until we've got a propositional form we don't have a complete sentence.
That is why a propositional form represents a class rather, than a proposition. The propositional form can be rewritten using the set theory symbols, so Px = {x|xєP}.
A proposition can be presented in two ways: a complese sentence, a sentence with quantor. If we've got so no quantor sentence like it's cold, then it can be viewed as p. But in case of quantor in a sentence like the Sun is heating, we've got a quantor so this sentence can be presented as ∃x.Sx&Hx.
If to take an incomplete proposition or a propositional form as x is a traitor, then instead of saying something about it we've got a description of class in which x presents a class of traitors. In other words we might take a class, but we've used a form like x is a traitor to describe it.
This propositional form can be presented as Px, Rxy, and it means x is a pony, x rides y. If x is a horse and y is a horse, then the first and second statements would be: Ph and Rhh so, horse is a pony, which is true, and horse rides a horse which isn't true. But it works only when the substitution is completed. Until we've got a propositional form we don't have a complete sentence.
That is why a propositional form represents a class rather, than a proposition. The propositional form can be rewritten using the set theory symbols, so Px = {x|xєP}.