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PHI 1101 Study Guide - Midterm Guide: Reductio Ad Absurdum, Enthymeme, Deductive Reasoning

Course Code
PHI 1101
Laura Byrne
Study Guide

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Statements (also known as: Assertions or Propositions)
*a sentence used to make a claim. They are capable of being either
true or false
being true or false distinguishes statements from sentences which
are not capable of being true or false: commands, questions and
expressions of volition (wishes)
Laws of Logic:
1. The Law of Non-Contradiction
2. The Law of the Excluded Middle/Law of Bivalence
Logicians and philosophers sometimes like to represent statements with
symbols: a, b, c or p, q, r
Ex. Socrates is a man. p
Socrates is not a man not-p (can also be written ~p or p)
The Law of Non-Contradiction
*States that it is impossible for both a proposition and its negation to
be true at the same time cannot assert both p and not-p at the
same time contradictions (p and not-p) cannot be true
Ex. Lassie is a dog. Lassie is not a dog. violating the Law of Non-
The Law of the Excluded Middle/the Law of Bivalence
*States that every proposition must be either true or false no middle
If p is true, not-p must be false
Sets of Propositions
Propositions can be combined in groups or sets.
Ex. Socrates is mortal.
Socrates is a philosopher.
Sets of propositions are either consistent or inconsistent.
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*A set of propositions is consistent if these propositions do not
contradict one another.
Ex. Lassie is a dog.
Lassie barks.
this set of proposition is consistent since it is possible for their
members to be true at the same time
*A set of propositions that contradicts each other.
Ex. Socrates is mortal.
Socrates is an Olympian God.
Consistency does not imply that all, or any, of the sentences in a consistent
set are true.
Two false statements can be consistent.
Ex. Socrates is immortal.
Socrates is an Olympian God.
To logically evaluate a set of propositions as consistent is only to see that it
is possible for them to be true at the same time, not that they are actually
*A logical relationship between two thoughts that occurs when one
thought supports or justifies or makes it reasonable to believe another
Indicators: since, thus, implies, consequently, because, it follows
that, given that
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