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PHI 1101 Study Guide - Midterm Guide: Principle Of Bivalence, Enthymeme, Deductive Reasoning


Department
Philosophy
Course Code
PHI 1101
Professor
Laura Byrne
Study Guide
Midterm

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2016-03-15
PHI 1101: Reasoning and Critical Thinking: Additional Concepts
Professor Laura Byrne
Department of Philosophy, University of Ottawa
Law of Excluded Middle
It is characteristic of the statements we are dealing with that they
obey the Law of Excluded Middle, also known as the Law of Bivalence,
which asserts that every statement must be either true or false. In other
words, any middle position between truth and falsity is excluded. From the
Law of Excluded Middle it follows that, for any given statement and the
negation of that statement, it must be the case that one of them is true and
one false. The reason for this is that if a statement cannot be anything
other than true or false it follows that if a statement is true, then its
negation must be false, and if a statement is false, then its negation must be
true.
Law of Non-Contradic tion
The statements we are dealing with also obey what is known as the
Law of Non-Contradiction, which says that it is impossible for both a
statement and its negation to be true at the same time. In other words, at
one and the same time, one cannot truthfully both assert and deny that
something is the case.
CONSISTENCY
Consistency is a property of a group, or set, of statements. A set of
statements is consistent if and only if it is possible for all of the statements
in that set to be true at the same time. Another way of saying this is that
these statements do not contradict one another. A set of statements is
inconsistent if it is not consistent, that is, if it is impossible for all the
statements in that set to be true at the same time.
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Notice that the definition of consistency does not imply that all, or
indeed any, of the statements in a consistent set of statements is in fact
true; two false statements can be consistent. To say that two statements
are consistent means simply that they both can be true at the same time,
not that they both are true here and now.
Example One: Consistent Set: Socrates is mortal.
Socrates is a man.
Example Two: Inconsistent Set: Socrates is mortal.
Socrates is immortal.
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