Lecture notes #1: Basic concepts
Reading: Chapter 1
I. Preliminaries
 Review syllabus
 Please buy book and SSG immediately and bring both to class every day
 Text very compact, and contains a lot of exercise.
 SSG has bullet point notes, breakdown of tests, additional answers to exercises, and extra
exposition.
 I do not assume you’ve had logic. If you have, some duplication at the beginning.
II. What is Logic?
 Quick definition: the study of reasoning
 Problem: other subjects study reasoning as well
1. Cognitive sciences
2. Communication studies
 Major difference: logic is normative, others mainly descriptive
 Logic = the normative study of reasoning, specifically, argumentation.
 Aristotle: one aspect of logic is its use as an organon
III. But what is an “argument”?
 Proposition = statement = a linguistic act that is T or F
 Compare: question, command
 Statements are usually expressed in declarative sentences, but don’t confound the two.
1. Tool vs. product
2. Different declaratives can express same statement
3. Same declarative can express different statements
4. Don’t need a sentence at all to make a statement
 Argument = a group of two or more statements, one of which (the conclusion) is c taken
to be evidentially supported by the others (the premises).
 Standard form…
 By itself, a given statement is neither a premise nor a conclusion. It becomes so
depending upon how it is used vis-à-vis other statements
IV. How many varieties of “evidential support” are there?
 Consensus: two—deductive validity, inductive strength.
 Lack of evidential support = fallacy
 Compare three arguments
 Define each
 Deductive logic = the study, involving explication and evaluation, of deductively valid
arguments.
 Inductive logic = the study, involving explication and evaluation, of inductively strong
arguments.
 This is a course in deductive logic only.
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Don’t confound the validity or invalidity of an argument with the truth or falsity of the
statements in it.
Sound = valid + true premises
V. What is “symbolic logic”?
 Theory of deduction:
1. Decision procedure
2. Proof procedure
3. Explanation (not merely a definition) of “validity”
 Historically, three major theories of deduction
1. Syllogistic/traditional/Aristotelian logic
2. Algebraic logic
3. Symbolic/mathematical/modern logic
 Early appearance: Frege 1879…Peano, Whitehead, Russell, Hilbert, Cantor, Church,
Godel, Turing major later players….
 Symbolic logic uses logistic (artificial) languages as a tool to accomplish the three goals
of any theory of deduction.
 We will develop a logistic language in stages, corresponding to major classes of
argument: sentential arguments; property arguments; relational arguments; identity
arguments
 Together these are referred to “First order logic” (FOL)
 Symbolic logic has many uses
1. Mathematics—investigate foundations
2. Philosophy—analytical tool to investigate issues
3. Computer science—logical circuit design, programming design and verification,
AI
4. Linguistics
VI. Final points
 Aristotle early on say difference between logic as organon vs. as an object of study
 Meta-logic = the study of various logistic systems, and how well they accomplish their
purposes
 My goal: give you a solid introduction to one classic version of FOL, with a focus on
proof competence, but with some meta-logical comments thrown in.
 Second course in symbolic logic is where you would do meta-logic explicitly
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