Psy 416:
Reasoning and Problem Solving
Primer on Logic and Logical Concepts
Go to Lecture 6 notes
Go to page 2 of Primer
Erwin M. Segal
Department of Psychology and
Center for Cognitive Science
State University of New York at
Buffalo
Logic was an attempt to describe normative
or correct reasoning. A widespread belief in AI, Cognitive Psychology,
and Cognitive Science is that there are procedures representing the way
people think which can be implemented on computers using logic type rules
directly (algorithms) or by finding other ways to implement logical principles.
The study of reasoning in this case is the study of "natural" logic. Much
reasoning is evaluated by the extent to which it conforms to logical analyses,
and much reasoning research in psychology is aimed at explaining the errors
people make when they attempt to solve logic type problems.
Logical reasoning focuses on one aspect of how human cognitive
performance can be judged. Do the statements that are presented together
in a single discourse hold together? Are the statements consistent with
one another; and if any conclusions are drawn, do they legitimately follow
from the other statements made? Are they logical or are they illogical?
We hope to clarify what these terms and other terms mean, and give at least
some simple examples of how to answer such questions. Logical analysis
is based on the structural or the formal
relations among the components of the arguments rather than the meanings
of the components. If two arguments have the same logical
form one cannot be logical and the other not, regardless of
their differences in meaning.
There are many different logics with many similarities
and some differences. Logics are formal systems that include principles
which identify well-formed formulas, a set of axioms, and rules of derivation,
which when correctly applied purportedly lead to correct conclusions. Different
logics may reason about categories, propositions, relations, time, tenses,
beliefs, necessity, events, etc.
I. General concepts:
Deduction--Applying a sequence of rules of inference
from a set of premises and from which a conclusion necessarily follows.
Induction--coming to a conclusion that is likely
from the premises. Usually coming to a conclusion about a universal or
a particular from previous instances of particulars.
Proposition: A concept that usually represents
a statement, a sentence, or an assertion. (E.g. The moon is made of
green cheese. 2+2 = 4. Five is greater than seven. Dr. Segal
teaches Psy 416. All men are mortal. It's better to have loved and
lost than never to have loved at all. Sammy Sosa didn’t hit any homeruns
yesterday. Oedipus loved his mother) Sentences which represent propositions
in most logics, should have a truth value;
Many logics are called two-value logics,
in that they assume that all propositions are either true or false.
In formal logic different kinds of
propositions are represented by well-specified structures or forms. In
any formal logical system a given representation of (form for) a proposition
should be clear and unambiguous. Such forms are often called well-formed
formulas or wffs.
Premise: A proposition that is assumed to be true
for the sake of a logical argument.
Argument: A sequence of propositions, starting
with premises, which purportedly justifies another proposition, called
a conclusion.
Syllogism: A set of (usually, but not necessarily,
two) premises followed by a conclusion; the classical form of an argument.
Validity: A syllogism, or any
argument, is valid
if the conclusion(s) drawn logically follow from the premises; otherwise
it is invalid. In a valid argument
if the premises are true, the conclusion is necessarily true.
Soundness: A sound
argument is a valid argument in which the premises are true.
Go to page 2 of Primer
Go to page 3
Go to Lecture 6 notes