ABSTRACT
Atomic propositions are non-decomposable statements that have to be interpreted as a single entity by either a true or false valuation. Symbols such as p, q and r might represent the following statements: https://www.w3.org/1998/Math/MathML"> p john is taller than mary q mary is taller than tim r john is taller than tim https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203211991/94c3b92a-0a16-4a4e-9014-02b93290d004/content/math_120_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and appropriate valuations for the statements are decided by a little extralogical activity such as applying a tape-measure to the people concerned. A brief examination of the statements reveals that the truth of statements p and q implies the truth of statement r, and this observation might be expressed as an implication https://www.w3.org/1998/Math/MathML"> p ∧ q → r https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203211991/94c3b92a-0a16-4a4e-9014-02b93290d004/content/math_121_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> This statement encodes something we know about the property of tallness: if it is true that john is taller than mary and that mary is taller than tim, it follows that john is taller than tim. There is nothing wrong with descriptions of this sort, but a problem becomes apparent when the same reasoning is applied to greater numbers of people. Separate atomic statements have to be written for another comparison, say s, t and u, and another formula is required to bind these statements together in an implication relationship like the one above.
