No new reading for Wednesday.

Exam #1 will be given in class on Friday. It covers Chapters 1 and 2 (except for chapter 2, section 6).

On Monday, I’ll give you a more detailed outline.

Formation Rules for LSLBase clause (f-sl): Every sentence-letter of LSL is a well-

formed formula (a wff)

Recursion clauses: (f-~): If p is wff then the result of prefixing ‘~’ to p is a wff.(f-&): If p and q are wffs, then placing ‘&’ between them and

enclosing the result in parentheses yields a wff.(f-v): If p and q are wffs, then placing ‘v’ between them and

enclosing the result in parentheses yields a wff.(f-→): If p and q are wffs, then placing ‘→’ between them

and enclosing the result in parentheses yields a wff.(f-↔): If p and q are wffs, then placing ‘↔’ between them

and enclosing the result in parentheses yields a wff.

Closure Clause: Nothing is a wff in LSL if it is not certified by the preceding rules.

Formation rules and parse trees

For any wff p, you can construct a parse tree starting with capital letters at the bottom and adding nodes using only the recursion rules until you reach the top, which has a single node p.

Any symbol string constructed in this way is a wff. And nothing that can’t be constructed in this way is a wff.

Subformulae

‘Formulae’ is the traditional plural form of ‘formula’

A subformula of p is any formula appearing at a node on p’s parse tree.

Scope and main connectives

The scope of a binary connective c is the subformula appearing at the node where c is introduced. A tilde’s scope includes all and only the symbols appearing in the node immediately below the node introducing the tilde.

The main connective of a formula is the last connective added to it, working upwards through the parse tree.

Complications

Outermost parentheses of the entire formula can be dropped.

Parentheses are never added when just a tilde is added.

Always give the tilde the smallest scope consistent with the presence of parentheses.

Tildes and Scope

p. 15: tildes take the smallest possible scope

Look immediately to the right of the tilde. If a sentence letter appears, the tilde’s scope is the sentence letter only. If there is an open parenthesis (or bracket), then everything within the group surrounded by that parenthesis and its partner is in the scope of the tilde.

Exercises, p. 40

About Exam #1

I. 6 True-False Questions about Validity and Soundness (worth two points each)

II. 4 Symbolizations, worth 2, 3, 3, and 4

pts.)

III. Symbolize an argument, worth 8 pts.

IV. 2 parse trees, worth 4 pts. each