| q ' means "proposition p is incompatible with proposition q", i.e., if both propositions p and q evaluate as true, then and only then p | q evaluates as false." After section ✸8 the Sheffer stroke sees no usage. Section ✸10: The existential and universal "operators": PM adds "(x)" to represent the contemporary symbolism "for all x " i.e., " ∀x", and it uses a backwards serifed E to represent "there exists an x", i.e., "(Ǝx)", i.e., the contemporary "∃x". The typical notation would be similar to the following: "(x) . φx" means "for all values of variable x, function φ evaluates to true" "(Ǝx) . φx" means "for some value of variable x, function φ evaluates to true" Sections ✸10, ✸11, ✸12: Properties of a variable extended to all individuals: section ✸10 introduces the notion of "a property" of a "variable". PM gives the example: φ is a function that indicates "is a Greek", and ψ indicates "is a man", and χ indicates "is a mortal" these functions then apply to a variable x. PM can now write, and evaluate: (x) . ψx The notation above means "for all x, x is a man". Given a collection of individuals, one can evaluate the above formula for truth or falsity. For example, given the restricted collection of individuals { Socrates, Plato, Russell, Zeus } the above evaluates to "true" if we allow for Zeus to be a man. But it fails for: (x) . φx because Russell is not Greek. And it fails for (x) . χx because Zeus is not a mortal. Equipped with this notation PM can create formulas to express the following: "If all Greeks are men and if all men are mortals then all Greeks are mortals". (PM 1962:138) (x) . φx ⊃ ψx :(x). ψx ⊃ χx :⊃: (x) . φx ⊃ χx Another example: the formula:✸10.01. (Ǝx). φx . = . ~(x) . ~φx Df. means "The symbols representing the assertion 'There exists at least one x that satisfies function φ' is defined by the symbols representing the assertion 'It's not true that, given all values of x, there are no values of x satisfying φ'". The symbolisms ⊃x and "≡x" appear at ✸10.02 and ✸10.03. Both are abbreviations for universality (i.e., for all) that bind the variable x to the logical operator. Contemporary notation would have simply used parentheses outside of the