Psy 416: Reasoning and Problem Solving
Primer on Logic and
Logical Concepts
page 1 of Primer
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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.
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