PHI 1101 Lecture Notes - Lecture 2: False Premise, Law Of Excluded Middle, Principle Of Bivalence
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Reasoning and Critical Thinking Part One
Statements: True --------- False
Sets: Consistent --------- Inconsistent
Arguments: Logically Strong (Inductively Strong, Deductively Valid) --------- Logically Weak
(Inductively weak, Deductively invalid)
→ Each gets more complex and builds on the one before
Definition: A statement is a sentence used to make a claim. Statements are capable of being either
true or false. Logic also calls them assertions or propositions.
→ A lot of what humans say are sentences
→ not all sentences are statements
→ This property of being either true or false distinguishes statements from sentences
which are not capable of being either true or false: commands, questions and expressions
of volition (wishes).
→ Statements are a subset
→ Commands can not be argued as being false
Concept ------> Statement
Property-------> True or False
Propositions → Socrates is a man (made a claim so it’s a statement)
Command → Be a man, Socrates
Question → Is Socrates a man?
Expression of violation → Oh, that Socrates were a man
Two Laws of Logic
1.) The Law of Non-Contradiction:
→ This law states that it is impossible for both a proposition and its negation to be true at the same
→ Ex: you passed and you failed the test a does not make sense, isn’t true
→ At the same time, one cannot truthfully both assert and deny that something is the case.
→ One 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. (Law of Non-Contradiction is being violated)
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2.) The Law of the Excluded Middle or the Law of Bivalence
→ This logical law states that every proposition must be either true or false (They are the only values)
→ Any alternative or middle position between truth and falsity is excluded.
→ Ex: organisms are either dead or alive
-2 valued (bivalence) logic
*1st law says you can’t have both, 2nd law says you can’t have options, it’s either one and the other*
-This law is like heads and tails (flipping a coin)
→ If a proposition is true, its negation must be false. If a proposition is false, its negation
must be true.
→ Ex: If “Socrates is a man” is true, then its negation, “Socrates is not a man,” must be
→ If p is true, not-p must be false.
Sets of Propositions
→ Propositions can be combined in groups or sets
→ A set is when you have at least 2 propositions
ex: Lassie is a dog. Lassie is brave (2 propositions)
→ Propositions are either true or false, whereas Sets of propositions are either consistent
Concept ----> Set
Property ----> Consistent or inconsistent
Definition of Consistency: A set of propositions is consistent if the propositions do not contradict
one another. All propositions in the set have to be true at the same time.
Example of consistent: Lassie is a dog. Lassie barks.
Example of inconsistent: Socrates is mortal. Socrates is immortal.
→ Be aware that consistency does not imply that all or any of the sentences in a
consistent set are true.
→ A proposition is consistent if it is possible for all of the propositions in the set to be true at the
same time. (just because it’s possible, doesn’t make it true)
→ Members in the set can’t contradict one another.
→ It does not violate the law of the excluded middle.
Definition: A relationship between two thoughts that occurs when one thought supports or justifies or
makes it reasonable to believe another thought.
→ logical relation: Sometimes we see that two statements are not random and that they
are linked. One thought supports another thought or makes it reasonable to believe that
the other thought is true.
example: Socrates is a man. Socrates is mortal.
explanation: Socrates is a man, therefore he is a mortal. It makes sense.
→ Inference is a logical relationship between thoughts. It’s the heart of reasoning.
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