For the purposes of the propositional calculus, propositions (utterances, sentences, assertions) are considered to be either simple or compound. Compound propositions are considered to be linked by sentential connectives, some of the most common of which are AND, OR, "IF ... THEN ...", "NEITHER ... NOR...", "... IS EQUIVALENT TO ..." . The linking semicolon " ; ", and connective BUT are considered to be expressions of AND. A sequence of discrete sentences are considered to be linked by ANDs, and formal analysis applies a recursive "parenthesis rule" with respect to sequences of simple propositions (see more below about well-formed formulas).
- For example: The assertion: "This cow is blue. That horse is orange but this horse here is purple." is actually a compound proposition linked by ANDs: " ( ("This cow is blue" AND "that horse is orange") AND "this horse here is purple" ) ".
Simple propositions are declarative in nature, that is, they make assertions about the condition or nature of a particular object of sensation e.g. "This cow is blue", "There's a coyote!" ("That coyote IS there, behind the rocks."). Thus the simple "primitive" assertions must be about specific objects or specific states of mind. Each must have at least a subject (an immediate object of thought or observation), a verb (in the active voice and present tense preferred), and perhaps an adjective or adverb. "Dog!" probably implies "I see a dog" but should be rejected as too ambiguous.
- Example: "That purple dog is running", "This cow is blue", "Switch M31 is closed", "This cap is off", "Tomorrow is Friday".
For the purposes of the propositional calculus a compound proposition can usually be reworded into a series of simple sentences, although the result will probably sound stilted.
Read more about this topic: Propositional Formula
Famous quotes containing the word propositions:
“If an angel were ever to tell us anything of his philosophy I believe many propositions would sound like 2 times 2 equals 13.”
—G.C. (Georg Christoph)
“It has often been argued that absolute scepticism is self-contradictory; but this is a mistake: and even if it were not so, it would be no argument against the absolute sceptic, inasmuch as he does not admit that no contradictory propositions are true. Indeed, it would be impossible to move such a man, for his scepticism consists in considering every argument and never deciding upon its validity; he would, therefore, act in this way in reference to the arguments brought against him.”
—Charles Sanders Peirce (1839–1914)
“We want in every man a long logic; we cannot pardon the absence of it, but it must not be spoken. Logic is the procession or proportionate unfolding of the intuition; but its virtue is as silent method; the moment it would appear as propositions and have a separate value, it is worthless.”
—Ralph Waldo Emerson (1803–1882)