Free-standing instances of the variables 'p' and 'q' cannot fill the argument-slots of truth-functions such as conjunction and material implication, which require complete sentences as arguments
Statements that express a full thought and can be judged as either true or false—not just fragments or isolated words.
conjunction(Argument about atomic parthood via directional contact)
The coming together or contact of atoms from different directions, used to test whether atoms have spatial parts.
truth-functions(in formal logic)
Logical operations (like 'and' or 'if-then') that take statements as input and produce a true or false output based on whether the input statements are true or false.
variables (p and q)(in formal logic)
Placeholder letters used in logic that stand in for any statement or sentence—think of them like blank slots you can fill with different claims.
Ramsey (1929c, [OT] 9) anticipated a possible reaction to his use of propositional variables and to the translation of (4.1)–(4.3) as (4.1*)–(4.3*). The objection is the following: (4.1*)–(4.3*) cannot be English* counterparts of English sentences because they are not well-formed. Free-standing instances, the objection goes, of the variables ‘p’ and ‘q’ cannot fill the argument-slots of truth-functions, such as conjunction and material implication, which need complete sentences as arguments. F